Inverse functions

Front

What is an inverse function?

Back

An inverse function reverses the operation 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 algebraically?

Back

To find the inverse of a function f(x), follow these steps: 1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Front

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

Back

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

Front

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

Back

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

Front

Back

Front

Find the inverse of f(x) = 1/4x - 7.

Back

f^-1(x) = 4x + 28.

Front

What is the composition of functions?

Back

The composition of functions f(g(x)) means applying function g first, then applying function f to the result.

Front

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

Back

None of these.

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

What is the relationship between a function and its inverse?

Back

If f is a function and f^-1 is its inverse, then f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.