##### Notes

This printable supports Common Core Mathematics Standard HSF-BF.A.1, HSF-BF.A.1c

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# Composite Functions (Grades 11-12)

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## Composite Functions

1.
Find $(f@g)(x)$ if $f(x) = 7x + 1$ and $g(x) = -2x +34$.
1. $-14x +35$
2. $-14x +239$
3. $5x +35$
4. $5x + 239$
2.
$f(x)= 2x+6 and g(x) = 4x+2$. Find $(g @ f)(x)$.
1. $8x+26$
2. $8x+10$
3. $6x+8$
4. $6x+12$
3.
$f(x) =7x+9 and g(x) = 4x-1$. Find $(f @ g)(x)$.
1. $28x+8$
2. $28x+16$
3. $28x+2$
4. $28x+35$
4.
$f(x) = 3x-12 and g(x) = 4x$. Find $(f @ g)(x)$.
1. $12x^2+48x$
2. $12x-48$
3. $12x-12$
4. $7x-12$
5.
If $f(x)=x^2$ and $g(x)=3x-1$, find $(g@f)(x)$.
1. $x^2 +3x-1$
2. $9x^2 -6x+1$
3. $9x^2 -1$
4. $3x^2 -1$
6.
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. $25x-3$
7.
$f(x) = sqrt(x+8) and g(x)= 8x-12$. Find $(f @ g)(x)$.
1. $2sqrt(2x-1)$
2. $8sqrt(x+8)-12$
3. $8sqrt(x-4)$
4. $2sqrt(2x+1)$
8.
Let $f(x) = 5x-2 and g(x)= (3x)/ (2+x)$. Find $(g@f)(x)$.
1. $(15x)/(x+2) - 2$
2. $(15x)/(2+5x)$
3. $(3x(5x-2))/(x+2)$
4. $(15x-6)/(5x)$
9.
$f(x)=6/(x-4) and g(x)= 5/(4x)$. Find $(f @ g)(x)$.
1. $(24x)/(5-16x)$
2. $(24x)/(5+16x)$
3. $(6x)/(5-16x)$
4. $(5x-20)/(24x)$
10.
Let $f(x) = 3x^2-5x and g(x)=sqrt(x+2)$. Find $(g@f)(x)$.
1. $3(x+2) - 5sqrt(x+2)$
2. $sqrt(3x^2-5x+2$
3. $-2x + 6$
4. $sqrt(3)x - (sqrt(5) -1) sqrt(x)$
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