Function Operations & Compositions

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 f(g(x))?

Back

To find f(g(x)), substitute g(x) into the function f. This means you take the output of g(x) and use it as the input for f.

Front

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

Back

The formula for (f + g)(x) is simply the sum of the two functions: (f + g)(x) = f(x) + g(x).

Front

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

Back

The formula for (f - g)(x) is the difference of the two functions: (f - g)(x) = f(x) - g(x).

Front

What is the formula for (f ⋅ g)(x)?

Back

The formula for (f ⋅ g)(x) is the product of the two functions: (f ⋅ g)(x) = f(x) * g(x).

Front

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

Back

The formula for (f / g)(x) is the quotient of the two functions: (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

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

Back

f(g(2)) = f(2^2 + 3) = f(7) = 2(7) = 14.

Front

If f(x) = 3x^2 - 2x + 1, what is f(1)?

Back

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

Front

What is the output of g(5) if g(x) = x - 2?

Back

g(5) = 5 - 2 = 3.

Front

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

Back

(f ° g)(x) = f(g(x)) = f(x^2 + 2) = 3(x^2 + 2) - 1 = 3x^2 + 6 - 1 = 3x^2 + 5.