Function Compositions

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find g(h(1)) if g(a) = 4a + 1 and h(a) = -3a + 2?

Back

First, find h(1): h(1) = -3(1) + 2 = -1. Then, find g(-1): g(-1) = 4(-1) + 1 = -3. So, g(h(1)) = -3.

Front

What is the formula for g(n) = 2n + 4?

Back

This is a linear function where the slope is 2 and the y-intercept is 4.

Front

How do you evaluate g(g(-6)) if g(n) = 2n + 4?

Back

First, find g(-6): g(-6) = 2(-6) + 4 = -8. Then, find g(-8): g(-8) = 2(-8) + 4 = -12.

Front

What does f(g(2)) mean if f(x) = 1/x and g(x) = 3x + 2?

Back

It means you first calculate g(2) = 3(2) + 2 = 8, then substitute this into f: f(8) = 1/8.

Front

What is the result of (f ∘ g)(2) if f(x) = 1/x and g(x) = 3x + 2?

Back

(f ∘ g)(2) = f(g(2)) = f(8) = 1/8.

Front

What is the significance of the notation f(f(0))?

Back

It indicates that you first evaluate f(0) and then use that result as the input for f again.

Front

If f(x) = x^2 - 3 and g(x) = x - 3, how do you find f(g(f(3)))?

Back

First, find f(3): f(3) = 3^2 - 3 = 6. Then, find g(6): g(6) = 6 - 3 = 3. Finally, find f(3): f(3) = 6.

Front

What is the output of f(f(0)) if f(x) = x^2 - 3?

Back

f(0) = 0^2 - 3 = -3, then f(-3) = (-3)^2 - 3 = 6.

Front

What is the composition of two functions?

Back

The composition of two functions f and g is a new function that applies g first and then f to the result of g.