Common Core Standard HSF-BF.A.1c Questions

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

For

$f(x) = 1/x$ and g(x) = x − 1, the domain of (f∘g)(x) is .

x > 1
x ≥ 1
x ≠ 1
x < 1

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

If f(x) = 3x − 2 and

$g(x) = (x + 2)/3$ , what is (g∘f)(4)?

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

For f(x) = x - 7 and g(x) = x² + 1, find (g∘f)(3).

17
-3
10
9

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$f(x)=6/(x-4) and g(x)= 5/(4x)$ . Find

$(f @ g)(x)$ .

$(24x)/(5-16x)$
$(24x)/(5+16x)$
$(6x)/(5-16x)$
$(5x-20)/(24x)$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Let

$f(x) = 5x-1 and g(x) = 3x^2 + 2x - 1$ . Find

$(g@f)(x)$ .

$75x^2 - 20x$
$15x^2+10x-6$
$75x^2-28x+2$
$25x-3$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

For

$(f@g)(x) = e^(-x^2 + 6)$ , which of the following are possible function rules of

$f(x)$ and

$g(x) ?$ There may be more than one correct answer.

$f(x) = e^x, \ \ g(x) = -x^2 + 6$
$f(x) = e^(-x+6), \ \ g(x) = x^2$
$f(x) = e^(-x^2 - 4x + 2), \ \ g(x) = x-2$
$f(x) = x^2, \ \ g(x) = e^(-1/2x^2 + 3)$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Given f(x)=2x+3 and g(x)=x−3(2), compute (f∘g)(9).

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Given f(x) = x² and g(x) = 3x, what is (f∘g)(−2)?

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

For f(x) = tan x and

$g(x) = π/4 − x$ , what is (f∘g)(

$π/4$ )?

0
-1
1
Undefined

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Given f(x) = cos(x) and g(x) = πx, find (f∘g)(

$1/2$ ).

$√2/2$
-1
0
1

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$f(x) = sqrt(x+8) and g(x)= 8x-12$ . Find

$(f @ g)(x)$ .

$2sqrt(2x-1)$
$8sqrt(x+8)-12$
$8sqrt(x-4)$
$2sqrt(2x+1)$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

For

$f(x) = 3x^2 - 1$ and

$g(x) = sqrt(2x-5)$ , find

$(g@f)(x)$ .

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Which of the following could be the function rules for

$f(x)$ and

$g(x)$ if

$(f@g)(x) = sqrt(x^3-8) ?$ There may be more than one correct answer.

$f(x) = sqrt(x), \ \ g(x) = x^2 - 8$
$f(x) = sqrt(x^2-8), \ \ g(x) = x$
$f(x) = sqrt(x-8), \ \ g(x) = x^3$
$f(x) = sqrt(x^3), \ \ g(x) = x-2$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Given

$(f∘g)(x)=∣2x−6∣,$ which combination is impossible?

$f(x)=∣x∣$ ,g(x)=2x−6
$f(x)=∣x-6∣$ ,g(x)=2x
$f(x)=∣2x∣$ g(x)=x−3
All are possible

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

If f(x) = |x| and g(x) = x − 5, what is (g∘f)(−3)?

2
-2
8
-8

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Given f(x) = 2x + 3 and

$g(x) = x^2 - 1$ , find (g∘f)(2).

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

If f(x) = 3x + 2 and

$g(x) = (x - 2)/3$ , find (g∘f)(5).

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$f(x) = 3x-12 and g(x) = 4x$ . Find

$(f @ g)(x)$ .

$12x^2+48x$
$12x-48$
$12x-12$
$7x-12$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

Find

$(f@g)(x)$ and state its domain if

$f(x) = 3x^2 + 5x - 3$ and

$g(x) = 4x-1$ .

$48x^2 - 4x - 5, \ \ RR$
$48x^2 - 19x, \ \ RR$
$3x^2 + 20x-8, \ \ x!=1/4$
$48x^2 - 4x - 5, \ \ x!= 1/4$

Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$(f@g)(x) = x^4 - 6x^2 + 7x + 9$ , which of the following are possible functions rules for

$f(x)$ and

$g(x) ?$ There may be more than one correct answer.

$f(x) = x^2 + 7x, \ \ g(x) = x^2 - 3$
$f(x) = x^2, \ \ g(x) = x^2 +7/3 x + 3$
$f(x) = x+3, \ \ g(x) = x^4 - 6x^2 + 7x + 6$
$f(x) = x^4 + x^3 - 17/4, \ \ g(x) = x - 1/4$

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Common Core Standard HSF-BF.A.1c Questions

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