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HSF.BF.A.1.c Tutor Intake — Function Composition

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·standard·hsf-bf-a-1c

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Concepts

Which statement best describes what $(f \circ g)(x) = f(g(x))$ means?

Multiply $f(x)$ and $g(x)$ together

Apply $g$ to $x$ first, then apply $f$ to that result

Apply $f$ to $x$ first, then apply $g$ to that result

Add the outputs of $f$ and $g$ at the same input

Let $f(x) = x + 1$ and $g(x) = x^{2}$ .

Complete the statement: $f(g(x)) = f(x^{2}) = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

simplified expression:

Let $f(x) = 2x$ and $g(x) = x + 3$ .

Which statement is true?

$f(g(x)) = g(f(x))$ for all $x$

$f(g(x)) = 2x + 6$ and $g(f(x)) = 2x + 3$ , so they are different

$f(g(x)) = g(f(x))$ because addition and multiplication commute

$f(g(x)) = 2x + 3$ and $g(f(x)) = 2x + 6$ , so they are different

Procedures

Use the values below.

$x$	$f(x)$	$g(x)$
1	4	2
2	3	1
3	2	5
4	6	3
5	1	4

Find $f(g(3))$ .

Use the values below.

$x$	$f(x)$	$g(x)$
1	4	2
2	3	1
3	2	5
4	6	3
5	1	4

Find $g(f(2))$ .

Let $f(x) = 3x - 1$ and $g(x) = x + 4$ .

Find the value of $f(g(2))$ .

Let $f(x) = x^{2}$ and $g(x) = x - 5$ .

Which expression equals $(f \circ g)(x)$ ?

$x^{2} - 5$

$(x - 5)^{2}$

$x^{2}(x - 5)$

$x^{2} - 5x$

Let $f(x) = \sqrt{x}$ and $g(x) = x - 1$ .

What is the domain of $f(g(x))$ ?

All real numbers

$x \geq 0$

$x \geq 1$

$x \neq 1$

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