Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function. It is denoted as (f∘g)(x) = f(g(x)).

Front

If f(x) = 2x + 3, what is f(5)?

Back

f(5) = 2(5) + 3 = 10 + 3 = 13.

Front

What does f(g(x)) represent?

Back

f(g(x)) represents the composition of function f with function g, meaning you first apply g to x, then apply f to the result.

Front

If g(x) = x^2 and f(x) = 3x, what is (f∘g)(2)?

Back

(f∘g)(2) = f(g(2)) = f(2^2) = f(4) = 3(4) = 12.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is (f∘g)(x), which means f(g(x)).

Front

If f(x) = x + 1 and g(x) = 2x, what is (g∘f)(3)?

Back

(g∘f)(3) = g(f(3)) = g(3 + 1) = g(4) = 2(4) = 8.

Front

What is the value of f(f(3)) if f(x) = x - 1?

Back

f(f(3)) = f(3 - 1) = f(2) = 2 - 1 = 1.

Front

If f(x) = 5x and g(x) = 2x - 1, what is f(g(1))?

Back

f(g(1)) = f(2(1) - 1) = f(1) = 5(1) = 5.

Front

What is the result of (g∘h)(x) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

(g∘h)(x) = g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

If f(x) = -x + 2, what is f(f(2))?

Back

f(f(2)) = f(-2 + 2) = f(0) = -0 + 2 = 2.