1 and g(x) 2 6 + 2. Let f(x) - - Find the following functions. Simplify your answers. f(g(x)) = g(f(x)) =

Q: x2-8 If fx)= X-4 where is f not differentiable?

A: Given the function

Q: x2 - 8 If f(x) = X-4 where is f not differentiable?

A: Find where is f not differentiable

Q: G' (x) = 2xex + x 2ex, and this is not equal to f (x). However, H'(x) = 2ex + 2xex - 2ex = 2xex = f…

A: Given Data The derivative function is G’(x)=2xeˣ+x2eˣ. The another derivative function is H’(x)=…

Q: 1 If f(x) = and g(x) =-, 2x +1 1 find f (g(x)) and its domain. - 2

A: Composite function :  A composite function is created when one function is substituted into another…

Q: 6. Given the function f(x)=x² find the equation of g(x) where f(x) is shifted to the right 2 units,…

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

Q: Let P=(x,y) be a point on the graph of y=x2-5  a) Express the distance d from P to the origin as a…

A: P=(x,y) be a point on the graph of y=x2-5

Q: 1) Let f(x) = –2x² – 3x + 2 f (x+h)-f(x) Find where h # 0 and simplify your answer as much h…

A: We have to find the value of function

Q: The function f is defined by f(x) = \25 – x² for -5 sx 5. (a) Find f'(x). (b) Write an equation for…

A: Given: fx=25-x2; x∈-5,5 we know that for finding derivative of given function, we differentiate…

Q: snip

A: Given: fx=1x and fgx=x+1x2-x

Q: 4. Given the functions h(x) = 3x - 4 find h(x) 5x + 2

A: Here we have to find inverse of function h(x).

Q: 6. Given the function f (x) = x² + x - 3, find f (x + 1) 7. h(x) = 2×+ 1, find h(3) 1 8. Given f (x)…

A:

Q: 1) f(x) = 5x and g(x) = x - 3, find f(2) + g(1)

A: Please see the below picture for detailed solution.

Q: given the function f(x)=4x^3 -5, we calculate f^-1 (x) to be

A: To find the inverse of

Q: Can you check it please?

A: To verify thesteps in the  simplification

Q: 3. Given f(x) = -7x-8-4sin(8)- 3e-6x – 4n² then determine the defining equation of f(x).

A: To determine the defining equation of f(x) from f'(x), we integrate f'(x) with respect to x.

Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

A:

Q: 2. If f(x) = g(x) × h(x) and f'(x) = -2(x – 7) + 1(-2x – 6) , find a possible equation for f(x)

A: see below the answer and explanation

Q: x-2 where is f not differentiable? If f(x) = x-3

A: f(x)=x2-2x-3   Vertical asymptote of the above function is x=3

Q: x-1' Find the value of the constant A for which the follo

A: Find the value of A

Q: x2 – 4 3. Do you agree with the contention that the functions f(x) = x + 2 and g(x) х — 2 are the…

A:

Q: 2. Derivative of f(x) = - 9x + 4 is: a) 9 b) - 9 c) 4 d) 0

A: Derivative of constant is 0

Q: 10.Given f(x)=2x-3 and g(x)= x² + 1, solve f[g(x)]

A: We have to find fgx where functions are given as: fx=2x-3 and gx=x2+1. Here we have to find…

Q: A function f satisfy the condition f(x) − f(x−1) = 4x − 9 . If f(5) = 18, what is the value of f(3)…

A:

Q: x- 2 if xS-2 2 1. Sketch: f(x) = - 2 2

A:

Q: 3) Find the intervals where the function is increasing and where it is decreasing. f(x) = x² - 6x²…

A:

Q: x2 – 2x +1 Let f(x) = then find f(h+ 1) x2 + x - 2

A: The given function is: f(x)=x2-2x+1x2+x-2 which can be simplified as: f(x)=(x-1)2(x+2)(x-1)…

Q: #2. Determine the equation for piecewise function f(x) given its graph below. -9-8-7-6-5-4-3 f(x) 5…

A: Given data:-

Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: [4 Let A = * 1. Find f (A), where f(x) = 2x3 + 3x2 + 4x + 5

A: Answer

Q: Find the domain of the function: f(x) = ln(3 - x)

A: The Domain of a function Includes all values of x for which the function is defined. We know that a…

Q: 1. Given f(x) = -2x and g(x) = x - 7, find g(f(2)). *

A: f(x)=-2x g(x)=x-7

Q: x² -1 ,find f'(x) and f"(x). x? - 3x+2 If f(x)= 4. „find f"(0). x-1 If f(x)= e* 5,

A:

Q: 4. Let f(x) = (6x – 1 if x 0* Find the indicated function values. (a) f(-3) (b) f (0) (c) f(4)

A: The given function is fx=6x-1  if  x<07x+3  if x≥0

Q: Q8: Calculating Derivatives from the Definition. f(x) = x2 – 3x - 1 %3D

A:

Q: Question in Image.

A:

Q: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: 6. Given the function ƒ (x) = x² + x − 3, find f (x + 1). 7. h(x) = 2x+ 1, find h(3) 1 8. Given f…

A:

Q: 1 For what value of x does the function f(x) = =x³ – 4x attain the absolute maximum - in the…

A: here option (c) is true on doing differentiation we get the  f'(x)=3x^2/3-4 f'(x) =x^2-4 put f'(x)…

Q: x2 – 4 3. Do you agree with the contention that the functions f(x) = x+ 2 and g(x) х— 2 are the same…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: f(x) = 4x^2-12x+7   how is this function concave wherever it is defined?

A: Given:

Q: The derivative of a function is g'(x) = 19 – 6x² and the graph of g(x) passes through the point P(3,…

A: To find  g(x)

Q: 2) f(x) = x + 5 glx) = -x - 5x Find f(g(-4))

A:

Q: 1. Find when the function is increasing and when it is decreasing. x2 – 9 f(x) = x2 – 16

A:

Q: Find the local and absolute extreme values of the function on the given interval. f(x) = x - 6x² +9x…

A: The given function is: f(x)=x3-6x2+9x+2, [2,4] Now, let…

Q: Find a value of the constant k, if possible, that will make the function continous everywhere if…

A: The objective is to find the value of k that will make the function continuous everywhere.

Q: (x-1)(x+4) What is the long-run behavior of the function y =- As x → 0 and as x → -

A:

Q: 1 The functionf is defined by f(x)= 2–Vx+ 5 for-5<x< 0. (i) Write down the range of f.

A: The objective of the question is find the range of the function f(x). And  solve the composition of…

Q: - 2x f(x) = [1] Express the following as a piecewise function: x- 2 Work: Solution: f(x)=

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.