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

If f(x) = √x and g(x) = x², what is (g∘f)(4)?

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

Given

$f(x) = 1/x$ and g(x) = x² + 1, the domain of (f∘g)(x) is:

All real numbers
x ≠ 0
x ≠ ±1
x ≠ −1

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

$f(x) = 2/x$ and g(x) = x + 3, find (f∘g)(1).

$1/4$
2
8
$1/2$

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

$f(x) =7x+9 and g(x) = 4x-1$ . Find

$(f @ g)(x)$ .

$28x+8$
$28x+16$
$28x+2$
$28x+35$

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

Find the domain of the composite function

$(f@g)(x) if f(x)=x^2 and g(x)=sqrt(x+2)$ .

$(-oo,oo)$
$(-2,oo)$
$[-2,oo)$
$(-oo,-2)$

Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c

$(f@g)(x) = 10x - 2$ , which of the following are possible function rules for

$f(x)$ and

$g(x) ?$ Choose all correct answers.

$f(x) = 10x + 10, \ \ g(x) = x - 12$
$f(x) = 2x-4, \ \ g(x) = 5x+1$
$f(x) = 8x-9, \ \ g(x) = 5/4 x - 11/4$
$f(x) = 1/2x - 3 \ \ g(x) = 20x + 2$

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

Which composition gives

$h(x)=(x−4)^3$ ?

$f(x)=x^3,g(x)=x−4$
$f(x)=x -4,g(x)=x^3$
$f(x)=x^3-4,g(x)=x$
Both A and C

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.

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

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

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