Functions and Transformations Answers

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What is the domain of the composite function?

{all real numbers}

{r | r ≠ 0}

{r | r > 0}

{r | r < 0}

n(m(x)) = n(x²) = x² –

–3

Because m(n(x)) is n(m(x)), the composition of m and n is not commutative.

is not equal to

is equal to

is less than

Let p(x) = x3 and q(x) = x + 5. If p(q(x)) and q(p(x)) are shown on the graph, which statements are true? Check all that apply.

Graph A represents p(q(x)).

The composition of functions p and q is not commutative.

Graph B represents q(p(x)).

Both p(q(x)) and q(p(x)) have the same domain.

Graph A represents q(p(x)).

m(n(x)) = m(x – 3) = ()²

–3

x – 3

The function is a result of the composition (g ∘ f)(x). If , what is f(x)?

Option

f(x) = x + 3

Option

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