Let f (x) = x³ – 5x² – 8 and let g be the inverse of f ( -

Q: 3a.

A:

Q: Find the inverse of f(x) = (x – })´, x > . f-1(x) = 1 2 2 2

A:

Q: Find the inverse of the function. f(x) = 9-2x^3 f^-1(x) =

A: THIS QUESTION CAN BE SOLVED USING THE CONCEPT OF INVERSE OF FUNCTION.

Q: Let f(x) = { 2x-3. 3x²+2, if x < 3 if x ≥ 3 be a piecewise function. Evaluate Sof 0 f(x)dx=

A: We can find the integration of the piecewise function as below.

Q: Find the inverse of f(x) = (x - 1)/(x + 1).

A: Given function:

Q: Show that the function f (x) =1- x is bijective and also find its inverse function.

A:

Q: Find the inverse of the function f(x) = x². f- (7) The domain of f- is |

A:

Q: Show that f (x) = x³ +1 is one-to-one and find its inverse function f-'(x).

A:

Q: Let ƒ (x) = x³ – 5x² – 8 and let g be the inverse of f (i.e. g (x) = f -1 (x).

A:

Q: Ex/ show that f(x) = x+7x + 4 x + 1 has an inverse. %3D

A: In this question we have to find whether the function has an inverse.

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find the inverse of f(x) f-¹(z) = . ✓ 3z + 1 -3x+4

A:

Q: Find a formula for the inverse of the function. f(x) = 8 – x², x > 0 f-1(x) = %3D

A:

Q: 3. Find the rule for the inverse of f(x) = X +1

A: Inverse of functions is given.

Q: Let f (x) = 5x, g(x) = 2x² + 1, & h (x) = 6x + 2., find (go f) (x). Show your work using the…

A: fx=5x, gx=2x2+1, hx=6x+2

Q: What is the inverse of the function of g(x) = x^3

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Q: Find the inverse of f(x)=-V4.x+1.

A:

Q: Find the function f(x) that satisfies the conditions f1) - | and f'x)= 2x+1

A: Given that: f(x) satisfies f(1)=1and f'(x)=2x+1(x2+x+1)3 We have to find the function f(x)

Q: VERIFY that f(x) and g(x) are inverses of each other giver 2x f(x) %3D x+ 2 and g(x) = 1- x

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Q: Find the inverse for f(x) = 12x + 2 f-(x) g(x) = 7x³ – 15 - g-1(x) 12 h(x) x + 15 h- (x) = j(x) = Va…

A:

Q: Find ao of the function f(x) = (n - x)2

A: The given function is: f(x)=14π-x2

Q: find the inverse of the function  a) f(x)=1-x^3 f^-1(x)= b)f(x)=8/x f^-1(x)=

A:

Q: Find a formula for the inverse of the function. f(x) = 2 + V4 + 5x f-1(x) = ||

A:

Q: Find the inverse of the function y = In (x - 2). %3D

A: y = f(x) = ln (x-2) ey = x-2 x = 2 + ey x = f-1(y) = 2 + ey

Q: 4. a) Find the inverse of f(x) = = 3 %3D 4-

A:

Q: The inverse function of f(x) = 4x + 2 is %3D f-1(2) =

A:

Q: Find the inverse 0f             y =f(x)= x2, if x ≥ 0. Graph f and f -1.

A: A function g is the inverse of function f if for y=fx,  x=gy Inverse of x2:y=x2Replace x and…

Q: Let flx)=-x²-x+6 and g(x)=2x+5 , find f(g\x))

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Q: Let f(x) = (x + 3)². Find the inverse of f restricted to [- 3, ∞). f(x) =

A:

Q: f(x) = 2x + 3 - g(x) = 5x +7

A:

Q: Let f(x) = 5x + 2 and g(x) = x² – 1. Find (gºf)(4) %3D %3D Compute the inverse of the following…

A:

Q: Find the inverse of f(x)=−5x−1 over -3x-2 f^-1(x) =

A: Let's find.

Q: Show that f(x) = (x16)2 has no inverse on the interval

A: Solution of the problem as follows

Q: Find the inverse of f (x) = x +b, where b is constant. How is the graph of f related to the graph f.

A: Inverse of functions return its original value for which a function gave output

Q: Let f(x) = 2 – Væ + 5. What is the inverse of f?

A:

Q: Find ao of the function f(x)=(-x)², 0≤x≤ 2π

A:

Q: Find the inverse of the function f(x) = – 5x² . f-'(x) = The domain of ƒ-' is

A: Solution:- let f(x)=y

Q: What is the inverse of the function f(x) = 3(x + 2)²-5, such that x < -2? OF-¹(x)=-2+. 3 5…

A:

Q: Find the inverse of f(x) = 11 x + 3. %3D f-'(x) =

A: Given:- f(x) = 11x+3 To find :- Inverse of f(x)  i.e. f-1(x)

Q: Verify graphically that the functions f(x) = 2x − 3 and g(x) = 12 (x + 3) are inversefunctions of…

A: Inverse function: If two function f(x) and g(x) are symmetric about the line y = x then f(x) and…

Q: let f(x)= 4x/2-x find inverse function of f

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Q: b) Verify that f(x) = 5x – 1 and g(x) = x+1 are inverse functions. 5 %3D

A:

Q: Find the inverse of f (x) = 4x2for x &gt;= 0.

A: The given function is, fx=4x2 To find the inverse of the function we solve the equation of the…

Q: 1- Vã y = x2-4x2 + 16V, x24 エ-2

A:

Q: Find the inverse of g(x) = x2 - 3 for x &gt;= 0.

A: Find the inverse of g(x) = x2 - 3 for x &gt;= 0.

Q: . Let f (x) = x* + 3x – 2, and let g(x) denote the inverse of f. Then g'(2) is equal to:

A:

Q: Determine where f(x) = x² – 2 is increasing and where it is decreasing.

A: Given: fx=x2-2 The graph of the given equation is,

Q: 2 a) Determine the inverse of the function f (x) = ÷+ +1. 3x %3D

A:

Q: f(x) = x² is inverse function on integer number?

A: The inverse is f-1(x) = √x

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.