Understanding Inverse Functions and Derivatives

The video tutorial explains how to solve a problem involving the inverse of a function and its derivative. It covers two parts: finding the value of f inverse of 6 without explicitly finding f inverse of x, and determining the derivative of f inverse at x equals 6. The tutorial reviews relevant concepts, uses a table of values to solve part A, and applies derivative rules to solve part B. Graphical representations are used to illustrate the solutions.

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

• f(x) = 1/(7x + 1)

• f(x) = 7x^2 + 1

• f(x) = sqrt(7x + 1)

• f(x) = 7x + 1

What is the value of f inverse of 6?

• 6

• 5

• 0

• 1

If f of a equals b, what does f inverse of b equal?

• f(b)

• f(a)

• a

• b

What is the graphical representation of the inverse function?

• A rotation around the origin

• A reflection across the line y = x

• A reflection across the y-axis

• A reflection across the x-axis

What is the relationship between the slopes of the original and inverse functions?

• They are equal

• They are squares

• They are negatives

• They are reciprocals

How is f prime of x expressed using a rational exponent?

• 7x + 1 raised to the power of 1

• 7x + 1 raised to the power of 1/2

• 7x + 1 raised to the power of -1/2

• 7x + 1 raised to the power of 2

What is the derivative of f inverse at x equals 6?

• 7

• 1/7

• 12/7

• 7/12

What is the value of f prime of 5?

• 6/7

• 7/12

• 12/7

• 7/6

What is the slope of the tangent line to the inverse function at the point (6, 5)?

• 12/7

• 7/12

• 1/12

• 7

What is the reciprocal of the slope of the tangent line to the original function at the point (5, 6)?

• 12/7

• 7

• 7/12

• 1/7