Function Operations

Front

What is function composition?

Back

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

Front

How do you find the value of (f ⋅ g)(x)?

Back

To find (f ⋅ g)(x), multiply the outputs of the functions f and g at x: (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 calculate (f - g)(x)?

Back

To calculate (f - g)(x), subtract the output of g from the output of f at x: (f - g)(x) = f(x) - g(x).

Front

What does it mean to evaluate f(g(x))?

Back

Evaluating f(g(x)) means to first find g(x) and then use that result as the input for the function f.

Front

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

Back

f(2) = 2^2 + 1 = 4 + 1 = 5.

Front

What is the output of (f + g)(0) if f(x) = 2x and g(x) = 3x + 1?

Back

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

Front

How do you find (f ⋅ g)(4) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

(f ⋅ g)(4) = f(4) * g(4) = (4^2 + 4) * (3(4) + 1) = 20 * 13 = 260.

Front

What is the result of (q - p)(-2) if p(x) = 3x + 4 and q(x) = 2x^2?

Back

(q - p)(-2) = q(-2) - p(-2) = (2(-2)^2) - (3(-2) + 4) = 8 - (-6 + 4) = 8 - (-2) = 10.

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is f(g(5))?

Back

f(g(5)) = f(5 - 2) = f(3) = 3(3) + 10 = 9 + 10 = 19.