Composite Functions & Operations

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, denoted as (f∘g)(x) = f(g(x)).

Front

How do you find (f*g)(x) for two functions f(x) and g(x)?

Back

To find (f*g)(x), multiply the two functions together: (f*g)(x) = f(x) * g(x).

Front

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

Back

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

Front

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

Back

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

Front

How do you evaluate (f∘g)(x)?

Back

To evaluate (f∘g)(x), first find g(x) and then substitute that result into f(x): (f∘g)(x) = f(g(x)).

Front

Given f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, find (f*g)(x).

Back

(f*g)(x) = 3x^3 - 14x^2 + 9x - 4.

Front

Given f(x) = -3x + 7 and g(x) = 2x^2 - 8, find g(f(x)).

Back

g(f(x)) = 18x^2 - 84x + 90.

Front

If f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f - g)(x).

Back

(f - g)(x) = x^2 + 8x + 1.

Front

If f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = 5x^2 + 6x - 1.

Front

What is the result of (f∘g)(0) if f(x) = 3x + 10 and g(x) = x - 2?

Back

(f∘g)(0) = 4.