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

Let

$f(x) = x^2 + 6 and g(x) = (x+8)/x.$ Find

$(g@f) (-7)$ .

-55/7
384/7
295/49
63/55

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

$f(x) = (8x+1) / (10x-5)$ and

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

$(f@g)(x)$ , simplified, and state its domain.

$(8sqrt(x-2)+1) / (5(2x-1)), \ \ [2,oo)$
$(8sqrt(x-2)+1) / (5(2x-1)), \ \ (-oo,1/2)uu(1/2,oo)$
$(16x + 10 sqrt(x-2) - 31) / (5(4x-9)), \ \ [2,9/4) uu (9/4,oo)$
$(16x + 10 sqrt(x-2) - 31) / (5(4x-9)), \ \ (-oo,9/4) uu (9/4,oo)$

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

Given

$(f∘g)(x)=1/(x^2−4 )$ and

$g(x)=x^2$ , find f(x).

$1/(x−4)$
$(1/x^2)−4$
$1/(x^2−4)$
$(1/x)−4$

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

If f(x) = cos x and

$g(x) = πx$ , what is (f∘g)(

$1/2$ )?

$π/2$
2
1
0

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

Given

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

Grade 11 Functions and Relations CCSS: HSF-IF.A.2, HSF-BF.A.1, HSF-BF.A.1c

$f(x)=3x-4$ and

$f(g(x))=x$ , then

$g(x)$ is

$1/(3x-4)$
$(x+4)/3$
$3-4x$
$4x-3$

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

Find

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

$f(x) = log(-x-5)$ and

$g(x) = sqrt(x)$ .

$log(-sqrt(x)-5), \ \ x>0$
$log(-sqrt(x)-5), \ \ x<0$
$log(-sqrt(x)-5), \ \ x>25$
This composite function is not possible.

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

If (f∘g)(x)=10x−2, which pair is valid?

f(x)=2x−4,g(x)=5x+1
f(x)=10x+10,g(x)=x−12
Both A and B
Neither A nor B

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

Given f(x) = 2x and g(x) = x + 3, what is (f∘g)(1)?

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

Given

$f(x) = x/2$ and g(x) = 2x, what is (f∘g)(5)?

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

If f(x) = log x and

$g(x) = 10^x$ , find (f∘g)(3).

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

Let

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

$(g@f)(x)$ .

$(15x)/(x+2) - 2$
$(15x)/(2+5x)$
$(3x(5x-2))/(x+2)$
$(15x-6)/(5x)$

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

$(f@g)(x) = x^2 + 2x + 4$ , which of the following could be the functions

$f(x)$ and

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

$f(x) = x^2 + 3, \ \ g(x) = x+1$
$f(x) = x + 2, \ \ g(x) = x^2 + 2x + 2$
$f(x) = x - 5, \ \ g(x) = x^2 + 2x + 9$
$f(x) = x^2 + 2, \ \ g(x) = 2x$

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

Given

$f(x)=∣x−5∣$ and g(x)=x+1, evaluate (f∘g)(3).

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

For f(x) = log x and g(x) = 10^x, what is (f∘g)(2)?

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

For f(x) = 4 - x and g(x) = x², find (f∘g)(2).

0
4
-4
2

Grade 11 Functions and Relations CCSS: HSF-IF.A.2, HSF-BF.A.1, HSF-BF.A.1c

For x = -2, evaluate f(g(x)) - f(0), given that:

$f(x) = 2x + 5$

$g(x) = 4x$

-11
6
-4
-16

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

Let

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

$(g@f)(x)$ .

$3(x+2) - 5sqrt(x+2)$
$sqrt(3x^2-5x+2$
$-2x + 6$
$sqrt(3)x - (sqrt(5) -1) sqrt(x)$

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

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