16. Find the inverse function of f. f(x) = x2 - 3, x 2 0 Then, use compositions of functions to verify the two functions are inverses of each other.

Q: Find the inverse of the function on the given domain. f (x) = (x – 16)2, [16, 0) ab sin (a) o (2) =…

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Q: 1. Is the function F(x) = {r³ - 3x2 +4x-2 an antiderivative of the function f(x) =x?-6x+4? Use the…

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

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Q: Find an equation for f(x) using the tangent function. f(x) = f(x) 12- 10 8. 6. 4 2 X 3 2 6. 6 3 6 -8…

A: The given graph is:   To find the equation for f(x).

Q: Consider the following function. g(x) = -x2 + 9x + 6 Find the first and second derivatives of the…

A: The function is given by gx =-x2+9x+6 To evaluate : The interval where the function is concave…

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

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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: 4. Let a be a real number such that 0 < a < 1, and let f(t) = eat – t where t e R. a) Find the…

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Q: but f'(x) is never equal to 0. Why

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Q: Differentiate  f and find the domain of f f(x)  =    ln ln ln x

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Q: I need help on question B) : Suppose i have  f(x) = -1/2x^2+9   How would I find the inverse…

A: fx=-12x2+9 Put y=fx Then y=-12x2+9

Q: (3) Let y = f(x) = x2 +1, evaluate the derivative of the inverse function x = f-(y) at y = 2. %3D

A: Given :           y=fx=x2+1

Q: Find the first derivative f' and the original function f. f"(x) = x³ – 18x, f' (1) = 0, ƒ(1) = 8…

A: Given query is to find f(x) from f"(x).

Q: Show that g : B → A, g(x) = √ln x is the inverse of f. Why is f^−1(x) 6 ≠ −√ln x?

A:

Q: Consider the following. g(x) = (5x – x³) h(x) = (3x + 4) f(x) = (5x – x³)(3x + 4) Find g'(x) and…

A: gx=5x-x3hx=3x+4fx=5x-x33x+4

Q: Find the first derivative f' and the original function f. f"(x) = x³ – 10x + 6, f' (0) = 7, f(0) = 2…

A: Note: according to our guidelines we can answer only first question

Q: Find the inverse of the function on the given domain. f(x) = (2 – 10)2. [(10, 0) b sin (a) f\(2) =

A: Solution: The objective is to find the inverse of the given function

Q: if f(x) = x² √In x² x . find the derivative of this function f'(x A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: Let f(x) = x + ln(x) and g(x) its inverse. Find g′(1).

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Q: Given the function f(x) = Vx – 4 has an inverse, find f-1(x). Then, ACCURATELY graph f(x), f-1(x)…

A: Given: f(x)=x-4. To Find: fx, f-1x and fof-1x

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

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Q: Suppose f is a one-to-one, differentiable function and its inverse function f^−1 is also…

A: We know the relation between f and f-1 is f(f-1(x))=x Then we differentiate both sides of it with…

Q: findthe domain of the function. f(x)=\sin e^{-x}

A: The domain of a function is the values of the variable that can be input into the function. The…

Q: 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1)' %3D c. f(x) = 4e*- x %3D

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: 十2, What is the inverse function of y = ? T-2 Oy= 2(+1) 7-1 %3D 2z-2 O y = -1 2(+1) O y= -1 2-1

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Q: 3. Find the derivative of the following function using the formula. f(x + h) – f(x) lim h a. f(x) =…

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Q: h) f(x) = ln (xe³z)

A: We will use the chain rule of differentiation and the product rule of differentiation to…

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: 6. Suppose that f(x) = g(y) + x²y³ r + y (a) Use implicit differentiation to compute a formula for y…

A: We differentiate above function with respect to x and f(x) and  g(x) are function of x and y

Q: (a) Express the new function m(x) = ln in terms of the original function g(x) In(x). m(x) :

A: Given- mx=lnx2and gx=lnx To find- The value of mx in terms of gx. Formula used- lnab=lna-lnb

Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

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Q: Find the first derivative f' and the original function f. "(x) = x' – 8x + 6, f'(0) = 5, f(0) = 8…

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Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: 1 If f(6) = 3, and f'(6) 2 Let f'(x) be the inverse function of f(x). (f ')'(3) = Write the equation…

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Q: 8) Find (f-1)'(a) for each (the derivative of the inverse of function f). f(x) = x³ + 2x + 3, a = 0…

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Q: 4. If y(T) = 1 – exp(-bNT), find the inverse function T = T(y). (Show me your work!)

A: Answer

Q: Find the first derivative f' and the original function f. f"(x) = x – 14x + 4, f' (0) = 8, f(0) = 10…

A: Solve

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

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Q: 11. Use the definition of the derivative to find f'(x) for the function f(x) = x2 + x + 2. Show your…

A: We have to find the derivative of the given function.

Q: 28. Find the inverse function f1 (x) if f(x) = 0.08x + VT 10 A) " (x - VT) (x - VT) 8 100 B) 8 10 C)…

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Q: 7) Show that the function ƒ(z) = z² +4 has no inverse function.

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Q: 1) 2 a) Let f(x)=√x +4. Use the definition of the derivative to find f'(x). Find f'(5) by two…

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Q: 12. Find inverse function of the following function: f :R→ R* i. defined by f(x) = e* 4x+1 f: R → R…

A: Solve for x, for finding value of inverse function.

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

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Q: Find a formula for the inverse of the function.\\ f(x) 1+e" 1-ez ' f' (æ) =

A: Let f(x)=y f(y)=x

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

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Q: Evaluate the derivative of the inverse function of f at the given value c) f(x) = Vx² + 4 find…

A: Givenf(x)=x2+43

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: