Inverse Functions and Their Derivatives

The video tutorial explains how to solve a problem involving the inverse of a trigonometric function, specifically f(x) = sin(x). It covers determining the value of the inverse function at a specific point without explicitly finding the inverse function, and calculating the derivative of the inverse function at a given point. The tutorial also includes a graphical representation of the function and its inverse, highlighting the relationship between the original function and its inverse.

What is the function f(x) given in the problem statement?

• f(x) = x^2

• f(x) = cos(x)

• f(x) = tan(x)

• f(x) = sin(x)

What is the interval for x in the given function f(x) = sin(x)?

• π/4 to 3π/4

• π/2 to 3π/2

• π/2 to π

• 0 to π

Which trigonometric function value is used to find the inverse function value in part A?

• sin(π/4)

• sin(π/3)

• cos(π/3)

• tan(π/6)

What is the value of f inverse of 3/2?

• π

• π/3

• π/2

• π/4

What is the formula used to find the derivative of the inverse function?

• 1 / f'(x)

• f'(x) / 1

• 1 / f'(f inverse of x)

• f inverse of x / f'(x)

What is the derivative of f(x) = sin(x)?

• sec(x)

• tan(x)

• -sin(x)

• cos(x)

What is the value of f inverse prime of 3/2?

• 1/2

• 2

• 1/√3

• √3

What is the slope of the tangent line to the inverse function at x = 3/2?

• 2

• 1/2

• 3

• 1

How is the graph of the inverse function obtained?

• By rotating the graph of f(x) by 90 degrees

• By reflecting the graph of f(x) across the line y = x

• By shifting the graph of f(x) upwards

• By scaling the graph of f(x) horizontally

What is the relationship between the slopes of the tangent lines to f(x) and its inverse?

• They are equal

• They are unrelated

• They are reciprocals

• They are negative reciprocals