Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, switching the roles of inputs and outputs.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, switch x and y, and solve for y.

Front

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

Back

f^-1(x) = (x - 3)/2.

Front

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

Back

It means reflecting the graph of the function over the line y = x.

Front

If f(x) = x^2, what is f^-1(x)?

Back

f^-1(x) = √x (for x ≥ 0).

Front

What is the relationship between a function and its inverse?

Back

If f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

Front

What is the inverse of f(x) = -4x - 12?

Back

f^-1(x) = -1/4x - 3.

Front

What does it mean to switch x's and y's in a function?

Back

It means to find the inverse function by interchanging the input and output values.

Front

If f(x) = 3x + 10, what is g(f(x)) if g(x) = ⅓x - 3?

Back

None of these.

Front

What is the line of reflection for inverse functions?

Back

The line of reflection is y = x.