Composition & Inverse Functions

Front

What is the composition of functions f(g(x)) if f(x) = 5x and g(x) = 2x - 1?

Back

10x - 5

Front

What does it mean to find the inverse of a function?

Back

The x's and y's are switched.

Front

Find h(f(-1)) if f(x) = 5x.

Back

-4

Front

What is the relationship between a function and its inverse?

Back

They are reflected over y=x, but they are not both functions.

Front

The inverse of a function has been reflected over which line?

Back

y = x

Front

Define composition of functions.

Back

The process of applying one function to the results of another function.

Front

If f(x) = 3x + 2, what is f(g(x)) if g(x) = x - 1?

Back

3(x - 1) + 2 = 3x - 1.

Front

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

Back

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

Front

How do you find the inverse of a function algebraically?

Back

Replace f(x) with y, switch x and y, and solve for y.

Front

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

Back

The domain of the inverse function is [0, ∞).