Algebra 2: Inverse Functions and Compositions

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function, meaning if f(x) takes x to y, then f⁻¹(y) takes y back to x.

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 then solve for y.

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted as fog(x), means applying g first and then applying f to the result.

Front

What does it mean if fog(x) = x for all x in the domain?

Back

It means that f and g are inverse functions of each other.

Front

How do you verify if two functions are inverses?

Back

By checking if fog(x) = x and gof(x) = x for all x in the domain.

Front

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

Back

f⁻¹(x) = (x - 3)/2.

Front

What is the inverse of f(x) = -x + 5?

Back

f⁻¹(x) = -x + 5.

Front

What happens to the coordinates of a point when finding the inverse of a function?

Back

The x and y coordinates are switched.

Front

What is the significance of the horizontal line test?

Back

If a horizontal line intersects the graph of a function more than once, the function does not have an inverse.

Front

What is the inverse of f(x) = 3x - 9?

Back

f⁻¹(x) = (x + 9)/3.