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

(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
$f(x) = sqrt(x+3)$ and $g(x)=2x$. Find $(f @ g)(4)$.
1. $2sqrt14$
2. $sqrt11$
3. $sqrt14$
4. $2sqrt7$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If $g(x) = 4/(2-x) and (g@f)(x) = -2/x^2$, find $f(x)$.
1. $(2x^2)/(x^2+1)$
2. $(x-2)/x^2$
3. $2x^2 + 2$
4. $-1/(2(x^2 - 2))$
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
What are possible function rules for $f(x)$ and $g(x)$, if $(g@f)(x) = 9x^2 - 15x -13 ?$ There may be more than one correct answer.
1. $f(x) = x-2, \ \ g(x) = 9x^2+21x-7$
2. $f(x) = 3x+2, \ \ g(x) = x^2 - 9x + 1$
3. $f(x) = 3x^2 -5x - 5, \ \ g(x) = 3x-2$
4. $f(x) = 3x^2 - 5x - 13, \ \ g(x) = 3x$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
$f(x) =7x+9 and g(x) = 4x-1$. Find $(f @ g)(x)$.
1. $28x+8$
2. $28x+16$
3. $28x+2$
4. $28x+35$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find the domain of the composite function $(f@g)(x) if f(x)=x^2 and g(x)=sqrt(x+2)$.
1. $(-oo,oo)$
2. $(-2,oo)$
3. $[-2,oo)$
4. $(-oo,-2)$
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If $(f@g)(x) = 10x - 2$, which of the following are possible function rules for $f(x)$ and $g(x) ?$ Choose all correct answers.
1. $f(x) = 10x + 10, \ \ g(x) = x - 12$
2. $f(x) = 2x-4, \ \ g(x) = 5x+1$
3. $f(x) = 8x-9, \ \ g(x) = 5/4 x - 11/4$
4. $f(x) = 1/2x - 3 \ \ g(x) = 20x + 2$
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 $(f @ g)(x)$.
1. $(24x)/(5-16x)$
2. $(24x)/(5+16x)$
3. $(6x)/(5-16x)$
4. $(5x-20)/(24x)$
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 $(g@f)(x)$.
1. $75x^2 - 20x$
2. $15x^2+10x-6$
3. $75x^2-28x+2$
4. $25x-3$
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.
1. $f(x) = e^x, \ \ g(x) = -x^2 + 6$
2. $f(x) = e^(-x+6), \ \ g(x) = x^2$
3. $f(x) = e^(-x^2 - 4x + 2), \ \ g(x) = x-2$
4. $f(x) = x^2, \ \ g(x) = e^(-1/2x^2 + 3)$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
$f(x) = sqrt(x+8) and g(x)= 8x-12$. Find $(f @ g)(x)$.
1. $2sqrt(2x-1)$
2. $8sqrt(x+8)-12$
3. $8sqrt(x-4)$
4. $2sqrt(2x+1)$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
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.
1. $f(x) = sqrt(x), \ \ g(x) = x^2 - 8$
2. $f(x) = sqrt(x^2-8), \ \ g(x) = x$
3. $f(x) = sqrt(x-8), \ \ g(x) = x^3$
4. $f(x) = sqrt(x^3), \ \ g(x) = x-2$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
$f(x) = 3x-12 and g(x) = 4x$. Find $(f @ g)(x)$.
1. $12x^2+48x$
2. $12x-48$
3. $12x-12$
4. $7x-12$
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 $g(x) = 4x-1$.
1. $48x^2 - 4x - 5, \ \ RR$
2. $48x^2 - 19x, \ \ RR$
3. $3x^2 + 20x-8, \ \ x!=1/4$
4. $48x^2 - 4x - 5, \ \ x!= 1/4$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If $(f@g)(x) = x^4 - 6x^2 + 7x + 9$, which of the following are possible functions rules for $f(x)$ and $g(x) ?$ There may be more than one correct answer.
1. $f(x) = x^2 + 7x, \ \ g(x) = x^2 - 3$
2. $f(x) = x^2, \ \ g(x) = x^2 +7/3 x + 3$
3. $f(x) = x+3, \ \ g(x) = x^4 - 6x^2 + 7x + 6$
4. $f(x) = x^4 + x^3 - 17/4, \ \ g(x) = x - 1/4$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
$f(x)= 2x+6 and g(x) = 4x+2$. Find $(g @ f)(x)$.
1. $8x+26$
2. $8x+10$
3. $6x+8$
4. $6x+12$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find $(g@f)(x)$ and state its domain if $f(x) = (3x-5)/(9x-1)$ and $g(x) = 3x + 4$.
1. $(9x+7) / (27x + 35), \ \ x!= -27/35$
2. $(9x+7) / (9x - 1), \ \ x!= 1/9$
3. $(9x+7) / (27x+35), \ \ x!= -35/27$
4. $(45x-19) / (9x-1), \ \ x!=1/9$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Select the possible function rules of $f(x)$ and $g(x)$ if $(f@g)(x) = x^2 - 4$. Choose all correct answers.
1. $f(x) = ln(x), \ \ g(x) = e^(x^2-4)$
2. $f(x) = ln(x^2), \ \ g(x) = e^(1/2 x^2 -2)$
3. $f(x) = ln(x^2 - 8), \ \ g(x) = e^(1/2 x^2 + 2)$
4. $f(x) = e^x - 8, \ \ g(x) = ln(x^2+4)$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If $f(x) = x^2 + 3$ and $g(x) = sqrt(x-4)$ find $(f@g)(x)$ and state its domain.
1. $x-1, \ \ x >= 4$
2. $sqrt(x^2 - 1), \ \ x < -1 or x > 1$
3. $x+1, \ \ x >= 4$
4. $x+1, \ \RR$
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