Inverse Functions + Domain and Range

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, replace f(x) with y, swap x and y, and then solve for y.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Find the inverse of the function g(x) = 4/x.

Back

g^(-1)(x) = 4/x.

Front

Graph the inverse function of y = (x + 3)^2.

Back

The inverse is y = √(x) - 3.

Front

What is the range of the function y = (x + 3)^2?

Back

The range is y ≥ -3.

Front

Find the inverse of the function f(x) = 2x - 3.

Back

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

Front

What is the domain of the function f(x) = 2x - 3?

Back

The domain is all real numbers.

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of a function is the range of its inverse, and vice versa.