Function Operations and Compositions Review

Front

What is the sum of two functions f(x) and g(x)?

Back

(f + g)(x) = f(x) + g(x).

Front

Given 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 function composition?

Back

Function composition is applying one function to the results of another function, denoted as (g∘f)(x) = g(f(x)).

Front

Given p(x) = 3x + 4 and q(x) = 2x^2, find q(p(-2)).

Back

q(p(-2)) = 8.

Front

What is the product of two functions f(x) and g(x)?

Back

(f * g)(x) = f(x) * g(x).

Front

If g(x) = 6x + 4 and f(x) = 3, find f(x) * g(x).

Back

f(x) * g(x) = 18x + 12.

Front

Given g(x) = 3x + 4 and h(x) = 3x - 1, find (g∘h)(x).

Back

(g∘h)(x) = 9x + 1.

Front

What is the value of f(g(4)) if f(x) = x^2 + x and g(x) = 3x + 1?

Back

f(g(4)) = 182.

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if for every x in their domain, f(x) = g(x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) for which the function is defined.