3.6 please can you show me all steps Verify that f has an inverse function. Then use the function f and the given real number a to find (f-1)'(a). (Hint: See Example 1. If an answer does not exist, enter DNE.)f(x) = x+ 2x³)a = -11(f-1)(-11) =Need Help?Read It

Given f(x)=127( x5 + 2x3 ). To check if the function f has an inverse function we need to show that…

Verify that f has an inverse function. Then use the function fand the given real number a to find (f-1y'(a). (Hint: See Example 1. If an answer does not exist, enter DNE.) f(x) = a = -11 (F-)(-11) = [ Need Help? Read It

Verify that f has an inverse function. Then use the function fand the given real number a to find (f-1y'(a). (Hint: See Example 1. If an answer does not exist, enter DNE.) f(x) = a = -11 (F-)(-11) = [ Need Help? Read It

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.8: one-to-one Functions And Their Inverses

Problem 2E: (a) For a Function to have an inverse, it must be______ So which one of the following functions has...

See similar textbooks

Related questions

Q: 5. Calculate the derivative of f(x) = Use this result to determine whether the sequ x2 + 1 an = n2.…

Q: 1. Consider the function f(x) = x³ – 3x?. a. Sign analyze f (x). b. Find the derivative, f'(x). C.…

Q: Consider the following function. f(x) = 6Vx Find the first and second derivatives of the function.…

Q: Q4: al State and prove the theorem of derivative of inverse functions then use the steps of the…

Q: Consider the function f(x) = 2x2+1. Find the equation of the tangent to the graph of f(x) at x = 2.…

A: Not sure why we need to calculate f inverse of 2. We do need to calculate the value of the…

Q: 1. Write the derivative formula for each function. Use proper notation and equal signs. 12 b. h(x)…

A: Hey, since there are multiple subparts posted, we will answer first 3 questions. If you want any…

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: We have given fx=1-x3-6x5 By differentiating the function, f'x=-3x2-30x4=-3x21-10x2 Now, we find the…

Q: 1. Determine if the function is even or odd x*+1 g(x) = f(x) = sin x x3-2x

Q: Consider the function, f(x) = (x + 1)ln(5x² + e). Without finding explicitly the inverse of f(x),…

A: Given : fx = x+1ln5x2+e

Q: Q3:- A. Find the Gamma function of [(1) using definition

Q: = (x),! %D (b) Use part (a) to find the derivative of f(x). 4 (X)d – (4 + x)f (a) Compute the…

Q: (a) By using definition of differentiation, find f'(x) when f(x)= 3x - 5x (b) Given f(x)= (log(4x –…

A: Given: fx=3x-5x2 we know that ddxxn=nxn-1 ..1

Q: The derivative of the function f is defined by f'(x) = x² – x – 2 cos (x2). If f(3) = 2, then use a…

Q: 1. Determine if the function is even or odd g(x) = f(t) = sin 21 x2-9

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=sin(2x)+17 To find: f'π2 and f'(π)

Q: Write a function newt (f, df, x0) which implements Newton's method to identify a root of the…

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: Givenf(x)=cos3x2To determine whether the…

Q: 23. Find the derivative of the function. f(x) = 6sin?(-5x8) %3D f'(x) = %3D

A: Here is the solution of the given problem. Derivative: By chain rule

Q: Use the inverse function theorem to find the derivative of g(x) = x + 4 1 g'(x) = where f(x) = g1(x)…

A: Question is solved. Here is its solution. g(x) = (x+4)/x

Q: Use any method to find the derivative of the following (the results do not need to be simplified):…

Q: 1. Find the differentiation of inverse function for the following functions. (a) f(x) = 2x³ - 5 (b)…

Q: A. What is the domain and the range of the inverse function of f(x) = 4[sin(n – 2x) – 1] %3D -

A: It is asked to find the inverse of the given function.

Q: The function f is defined by f(x) = x² + 2 cos (3x + 3x). What is the average rate of change of f'…

A: Average rate of change of a function f on [a,b] is given by f(b)-f(a)b-a. Computing f(10) and f(3).…

Q: Suppose f : R → R is a C1 function such that f(-5) = 5 and f'(-5) Theorem states that x is a…

A: Let f(x) =ax+b then find value of a and b. Then find inverse of f(x).

Q: b\ State and prove the theorem of (derivative of inverse functions), then use it to answer these…

A: We have to state and prove the theorem of derivative of inverse functions and find ddxf-1x1 fx=logax…

Q: Consider the following function. f(x) = x + 4x – 2, (1, 3) (a) Find an equation of the tangent line…

A: Given function is fx=x2+4x-2 and point is (1,3). Differentiating the given function with respect to…

Q: Use Theorem on the derivative of the inverse function to find g'(a), where g= f-1. Calculate g(x)…

A: Here we have to find the inverse function and then its domain and range.

Q: Q3/Discuss the behavior of the following function as x 0: f) = sinx

A: Please rate and feel free to ask any query about any part of the question

Q: 1. Consider the function f ( x ) = 1 + 1/10 x3 + 1/25 x5 . Select any point ( a , f -1 ( a ) ) on…

A: Given function : f(x)=1+110x3+125x5 To solve the given problem first we need to find the inverse of…

Q: Find the first and second derivative of the function. Check to see that your answers are reasonable…

Q: Consider the following function. f(x) = Find the first and second derivatives of the function. g'(x)…

A: Given, f(x) =x + 5x - 5

Q: Consider the following function. g(x) = 3x3 - 3x Find the first and second derivatives of the…

A: Given, gx = 3x3-3x We have to find the first and second order derivative and the intervals of…

Q: 3. Let g(x) = [ v V1+t dt for r > 1. Determine whether g has an inverse function. Note: if an…

A: *As per our guidelines we are allowed to answer only 1 question at a time. Kindly please re-post…

Q: 3. Find the derivative of the following a) f (x)=x² sin (5x) (" \ b) ƒ (x)=e %3D e) f(x)=…

A: Part (a)

Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: 1. Find the derivative of f(x) = e" (x² – 1)ª. Make any obvious simplifications.

Q: 27) Find the inverse functionf of f with its domain and range. f(x) = cos(x – 3) + 2; 3<x<n+ 3 %D

A: Given that, f(x)=cos(x-3)+2 , 3≤x≤π+3 Domain of f(x)=[3,3+π] Range of f(x):- Range of f(x)=[1,3]…

Q: 2 If f(- 4) = – 1, and f'(– 4) = Let f (x) be the inverse function of f(x). (f ')'(- 1) = %3D Write…

Q: b\ State and prove the theorem of (derivative of inverse functions), then use it to ans these…

Q: b\ State and prove the theorem of (derivative of inverse functions), then use it to answer these…

A: We have to find the derivatives of the functions

Q: Consider the following function. x + 5 x - 5 f(x) = Find the first and second derivatives of the…

A: Quotient rule of differentiation:

Q: 4. Find the local maximum and minimum values of f,using both the First and the Second Derivative…

Q: 1 18. Find the derivative of f(x) = by the definition. %3D Itg MacBook Air 888 %24 &

Q: a) Given f(x) =- 3Vx + 2 Find f'(x) using the definition of derivative.

Q: Use the product rule to find the derivative of (82° – 3x*) (7e" – 1) Use e^x for e". You do not need…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: 3 If f(8) = 4, and f'(8) %3D - Let f-(x) be the inverse function of f(x). 1 Hint: (f-)'(z) =…

Q: 8. Find f '(2) if f(x) = [g(x)]*, and g(x) = x + 2

A: g(x) = x+2 f(x) = [g(x)]4 f(x) = (x+2)4

Q: The range of the function f(x)=2- sin 1x is: O a. [-1,3] O b. [-2,2] Oc. [-3,2] O d. [1,3] O e.…

A: We need to find the range of the function f(x). Range of Sine inverse x is (-pi/2 to pi/2).

Q: 3 If f( – 6) = 3, and f'( – 6) = %3D Let f'(x) be the inverse function of f(x). (f¯')'(3) = Write…

Question

3.6 please can you show me all steps

Verify that f has an inverse function. Then use the function f and the given real number a to find (f-1)'(a). (Hint: See Example 1. If an answer does not exist, enter DNE.)
f(x) = x+ 2x³)
a = -11
(f-1)(-11) =
Need Help?
Read It

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Pythagoras' Theorem$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

(a) For a Function to have an inverse, it must be______ So which one of the following functions has an inverse? f(x)=x2g(x)=x3 (b) what is the inverse of the function that you chose in part(a)?
Why do we restrict the domain of the function f(x)=x2 to find the function's inverse?
How do you find the inverse of a function algebraically?
Expression for the inverse of f(x) = e^(3x+1) f^-1(x) =?
Find a formula for the inverse function of h(x)=2e3x . Verify that h-1(h(0))=0
Consider the function f(x) = 2x2+1. Find the equation of thetangent to the graph of f(x) at x = 2. when calculating f!(2)(f inverse of 2) use first principles.
(a) Find the inverse function of f(x)=7x-6. f^-1(x)= ? (b) The graphs of f and f^-1 are symmetric with respect to the line defined by y=?
is given the function f (x) = 6-3x, its inverse function at the point x = -3, so f-¹ (-3) =
The function f(x) = √x is one-to-one. For the function,a. Find an equation for f -1(x), the inverse function.b. Verify that your equation is correct by showing thatf( f -1(x)) = x and f -1( f(x)) = x.