Combination & Composition of Functions Flashcard

Front

Define combination of functions.

Back

The combination of functions refers to the process of adding, subtracting, multiplying, or dividing two functions to create a new function.

Front

What is composition of functions?

Back

Composition of functions is the operation where one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

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

Front

Calculate (f - g)(x) if f(x) = 2x + 3 and g(x) = x - 1.

Back

(f - g)(x) = (2x + 3) - (x - 1) = x + 4.

Front

What is the formula for (f * g)(x)?

Back

(f * g)(x) = f(x) * g(x), which means multiplying the outputs of f and g for the same input x.

Front

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

Back

(f / g)(x) = 3x / (2x^2) = 3 / (2x) for x ≠ 0.

Front

Find f(g(2)) if f(x) = x^2 and g(x) = 3x + 1.

Back

g(2) = 3(2) + 1 = 7; then f(g(2)) = f(7) = 7^2 = 49.

Front

What is the result of f(x) - g(x) if f(x) = x^2 + 4 and g(x) = 2x?

Back

f(x) - g(x) = (x^2 + 4) - 2x = x^2 - 2x + 4.

Front

If f(x) = x + 5 and g(x) = 2x - 3, what is (f + g)(1)?

Back

(f + g)(1) = (1 + 5) + (2(1) - 3) = 6 + 1 = 7.

Front

What is the value of (f - g)(x) if f(x) = 4x^2 and g(x) = x^2 + 1?

Back

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