Inverse Functions

Front

What does it mean to find the inverse of a function?

Back

The x's and y's are switched.

Front

Find the inverse of the function f(x) = 3x − 5.

Back

f⁻¹(x) = (x + 5)/3.

Front

What operation allows us to verify if functions are inverses?

Back

Composing.

Front

Find g(f(x)) for f(x) = 3x + 10 and g(x) = ⅓x - 3.

Back

None of these.

Front

Find the inverse of f(x) = -4x - 12.

Back

f⁻¹(x) = -1/4x - 3.

Front

What is an inverse function?

Back

A function that reverses the effect of the original function.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

How do you find the inverse of a function algebraically?

Back

Replace f(x) with y, switch x and y, and solve for y.

Front

What is the graphical representation of inverse functions?

Back

They are reflections over the line y = x.

Front

If f(g(x)) = x, what does this imply about f and g?

Back

f and g are inverse functions.