5.5 - 5.6 Flashcard Review - Alg 2

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).

Back

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

Front

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

Back

(g(x) / f(x)) = (x - 2) / (x + 3).

Front

Given f(x) = 9 - 3x and g(x) = 5x - 7, find f(x) + g(x).

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

If f(x) = x^2 + 9 and g(x) = x - 9, find f(x) - g(x).

Back

f(x) - g(x) = (x^2 + 9) - (x - 9) = x^2 - x + 18.

Front

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

Back

g(f(x)) = g(-3x + 7) = 2(-3x + 7)^2 - 8 = 18x^2 - 84x + 90.

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted as f(g(x)), is the application of g first, followed by f.

Front

Define a function. Give an example.

Back

A function is a relation that assigns exactly one output for each input. Example: f(x) = 2x + 3.

Front

What is the difference between f(x) and g(x)?

Back

The difference f(x) - g(x) is the result of subtracting the output of g from the output of f.

Front

What does it mean for two functions to be equal?

Back

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

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.