Inverse Linear Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y back to x.

Front

How do you find the inverse of a function?

Back

1. Replace f(x) with y. 2. Switch x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

What is the inverse of f(x) = 2x + 3?

Back

f⁻¹(x) = (x - 3)/2.

Front

Are the functions f(x) = 3x + 8 and g(x) = (x - 8)/3 inverses of each other?

Back

Yes, they are inverses.

Front

What does it mean if two functions are inverses?

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain, then f and g are inverse functions.

Front

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

Back

Replace f(x) with y.

Front

What is the inverse of f(x) = 1/4x - 7?

Back

f⁻¹(x) = 4x + 28.

Front

If f(x) = x + 5, what is f⁻¹(x)?

Back

f⁻¹(x) = x - 5.

Front

True or False: The inverse of a function is always a function.

Back

False. The inverse of a function is not a function if it does not pass the vertical line test.

Front

What is the vertical line test?

Back

A method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.