Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if the function f takes an input x to produce an output y, then the inverse function f^-1 takes y back to x.

Front

If f(x) = x + 5, what is f^-1(x)?

Back

f^-1(x) = x - 5.

Front

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

Back

It means to switch the x's and y's in the function.

Front

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

Back

f^-1(x) = (x + 5) / 3.

Front

What is the inverse of the function f(x) = 2x + 4?

Back

f^-1(x) = (x - 4) / 2.

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Front

If f(x) = 5x + 1, what is f^-1(x)?

Back

f^-1(x) = (x - 1) / 5.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function's graph across the line y = x.

Front

If f(x) = x^2, does it have an inverse?

Back

No, f(x) = x^2 is not one-to-one, so it does not have an inverse unless restricted to x >= 0.

Front

What is the inverse of f(x) = 4x - 8?

Back

f^-1(x) = (x + 8) / 4.