Inverse Functions 21

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. The resulting equation is the inverse function.

Front

What is the relationship between a function and its inverse?

Back

The graph of a function and its inverse are reflections of each other across the line y = x.

Front

If f(2) = 5, what is f^-1(5)?

Back

f^-1(5) = 2, because the inverse function reverses the output back to the input.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^-1(x).

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

How do you determine if a function has an inverse?

Back

A function has an inverse if it is one-to-one, meaning that it passes the horizontal line test (no horizontal line intersects the graph more than once).

Front

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

Back

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

Front

What is the effect of a negative sign in front of a function?

Back

A negative sign in front of a function reflects the graph across the x-axis.