2B Composition of Functions and Operations

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean to compose functions?

Back

Composing functions means applying one function to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

Evaluate f(x) = x^2 - 5x at x = 4.

Back

f(4) = 4^2 - 5(4) = 16 - 20 = -4.

Front

Given g(a) = 4a + 1 and h(a) = -3a + 2, find g(h(1)).

Back

g(h(1)) = g(-1) = 4(-1) + 1 = -4 + 1 = -3.

Front

What is the formula for g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

What is the output of q(f(5)) if f(x) = x^2 - 5x?

Back

f(5) = 5^2 - 5(5) = 25 - 25 = 0; q(0) = 81.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the input and output values and solve for the new output.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.