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

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

Find

$(f@g)(x)$ if

$f(x) = 7x + 1$ and

$g(x) = -2x +34$ .

$-14x +35$
$-14x +239$
$5x +35$
$5x + 239$

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

Find

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

$f(x) = sqrt(x + 8)$ and

$g(x) = 2x^2 - 12$ .

$sqrt(2x^2 - 4), \ \ x>=sqrt(2)$
$sqrt(2x^2 - 4), \ \ x <= -sqrt(2) or x >= sqrt(2)$
$sqrt(2x^2 - 4), \ \ x>=2$
$sqrt(x-4), \ \ x>=4$

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

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

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

$f(x)=1/x$ and g(x)=x−5, find (f∘g)(2).

$-1/3$
$1/3$
-3
3

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

Find the domain of the composite function

$f(g(x))$ .

$f(x)= x+3$

$g(x)= 2/(x+6)$

$(-oo,3) uu (3,oo)$
$(-oo,oo)$
$(-oo,-6) uu (-6,3) uu (3,oo)$
$(-oo,-6) uu (-6,oo)$

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

For

$f(x) = e^(x + 3)$ and

$g(x) = 1/(x-2)$ , find

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

$e^(x+1), \ \ RR$
$e^(1 \ // \ (x+1)), \ \ x != -1$
$e^((3x-5) \ // \ (x-2)), \ \ x != 2$
$1/(e^(x+3) - 2), \ \ x != ln(2) -3$

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

For

$f(x)=1/x$ and g(x)=x−3, the domain of (f∘g)(x) is:

All real numbers
x≠0
x≠3
x>3

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

Which composition results in h(x)=(3x+1)4?

$f(x)=x^4, g(x)=3x+1$
$f(x)=3x^4+1, g(x)=x$
$f(x)=3x^4, g(x)=x+1$
$f(x)=3x+1, g(x)=x^4$

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

$f(x)= -5x , g(x)= 4x - 15$ . Find

$f(g(3))$ .

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

$f(x) = 4x^2 - 3x - 7$ and

$g(x) = ln(x + 6)$ , find

$(g@f)(x)$ and its domain.

$ln(4x^2 - 3x - 1), \ \ x > -6$
$ln(4x^2 - 3x - 1), \ \ x > 1$
$ln(4x^2 - 3x - 1), \ \ x < -1/4 or x > 1$
$ln(4x^2 - 3x + 1), \ \ RR$

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

If f(x)=3x+1 and

$g(x)=x^2−2$ , what is (f∘g)(2)?

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

Given

$f(x)=∣x∣$ and

$g(x)=x^2−4$ , find (f∘g)(−3).

5
- 5
13
- 13

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

Let

$f(x)=x^2$ and

$g(x)=x-3$ . Find

$(g@f)(3.5)$ .

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

Find

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

$f(x) = x^3 + 2x^2 - 8x + 1$ and

$g(x) = root[3](x)$ .

$x + 2root[3](x^2) - 8root[3](x) + 1, \ \ RR$
$x + 2root[2](x^3) - 8root[3](x) + 1, \ \ x >= 0$
$x + 2x^2 - 8x + 1, \ \ RR$
$x + 2root[3](x^2) - 8root[3](x) + 1, \ \ x >= 0$

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

Let

$f(x)=1/x$ and

$g(x)=x^2+4$ . Find (f∘g)(2).

$1/8$
$1/6$
$1/4$
$1/2$

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

$(f∘g)(x)=∣x−5∣$ and

$f(x)=∣x∣$ , find g(x).

x−5
x+5
5 - x
$sqrt x-5$

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).

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

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

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