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

Back

g(f(2)) = g(2(2) + 3) = g(7) = 7^2 = 49.

Front

What is the formula for adding two functions f(x) and g(x)?

Back

The formula for adding two functions is (f + g)(x) = f(x) + g(x).

Front

If f(x) = 3x - 1 and g(x) = x + 4, find (f + g)(x).

Back

(f + g)(x) = (3x - 1) + (x + 4) = 4x + 3.

Front

What is the formula for subtracting two functions f(x) and g(x)?

Back

The formula for subtracting two functions is (f - g)(x) = f(x) - g(x).

Front

If f(x) = x^2 and g(x) = 5x, find (f - g)(x).

Back

(f - g)(x) = x^2 - 5x.

Front

What is the composition of functions f(x) and g(x) when f(x) = x + 1 and g(x) = 2x?

Back

(f ∘ g)(x) = f(g(x)) = f(2x) = 2x + 1.

Front

If f(x) = x^2 and g(x) = 3x + 1, find g(f(1)).

Back

g(f(1)) = g(1^2) = g(1) = 3(1) + 1 = 4.

Front

What is the value of g(f(-2)) if f(x) = x + 3 and g(x) = x^2 - 1?

Back

g(f(-2)) = g(-2 + 3) = g(1) = 1^2 - 1 = 0.

Front

If f(x) = 4x and g(x) = x - 2, find (g ∘ f)(x).

Back

(g ∘ f)(x) = g(f(x)) = g(4x) = 4x - 2.