Inverse & Function Composition Review

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) takes x to 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, replace f(x) with y, swap x and y, and solve for y.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function has an inverse that is also a function. If any horizontal line intersects the graph more than once, the function does not have an inverse that is a function.

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverses of each other?

Back

Yes, they are inverses because f(g(x)) = x and g(f(x)) = x.

Front

What is the composition of functions?

Back

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

Front

If f(x) = x^2 and g(x) = √x, are they inverses?

Back

No, because f(g(x)) = x and g(f(x)) = x only for x ≥ 0.

Front

What is the notation for the inverse of a function f?

Back

The notation for the inverse of a function f is f⁻¹.

Front

How do you verify if two functions are inverses?

Back

To verify, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the range of the inverse function if the original function has a domain of [0, ∞)?

Back

The range of the inverse function will be [0, ∞) if the original function is one-to-one.

Front

What is the inverse of the function y = 5^x - 8?

Back

The inverse is y = log₅(x + 8).