Inverse Functions and Compositions Quiz

What is the first step in finding the inverse of a function algebraically?

• Switch x and y

• Switch f(x) with y

• Solve for y

• Divide by the coefficient of x

Why is it important to write functions in slope-intercept form?

• To find the domain and range

• To verify if they are linear functions

• To make them easier to graph

• To simplify calculations

What does a composition of functions involve?

• Multiplying two functions

• Using the output of one function as the input for another

• Subtracting one function from another

• Adding two functions together

How can you verify if two functions are inverses using compositions?

• Ensure both compositions equal the identity function

• Find their derivatives

• Check if their graphs intersect

• Compare their domains

What is the result of the composition f(g(x)) if f and g are inverses?

• 0

• x

• g(x)

• f(x)

In the example where y = 4x, what is the inverse function?

• y = 1/4x

• y = 4x + 1

• y = x/4

• y = -4x

What is the reciprocal of 1/2 used for in finding inverses?

• To subtract from both sides

• To divide both sides

• To multiply both sides

• To add to both sides

When switching x and y in the function y = -3x + 2, what is the next step?

• Add 2 to both sides

• Subtract 2 from both sides

• Multiply by -3

• Divide by 3

What is the slope of the function y = -2x + 3 after finding its inverse?

• -2

• 2

• 1/2

• -1/2

In the function y = 1/2x + 2, what operation is performed after switching x and y?

• Add 2 to both sides

• Multiply by 2

• Subtract 2 from both sides

• Divide by 2