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# Understanding Composite Functions (Grades 11-12)

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## Understanding Composite Functions

1.
$f(x)= -5x , g(x)= 4x - 15$. Find $f(g(3))$.
1. 18
2. -75
3. -15
4. 15
2.
$f(x) = sqrt(x+3)$ and $g(x)=2x$. Find $(f @ g)(4)$.
1. $2sqrt14$
2. $sqrt11$
3. $sqrt14$
4. $2sqrt7$
3.
Let $f(x) = x^2 + 6 and g(x) = (x+8)/x.$ Find $(g@f) (-7)$.
1. -55/7
2. 384/7
3. 295/49
4. 63/55
4.
If $f(x)=3x+7$ and $g(x)=2x-5$, find $g(f(-3))$.
1. -26
2. -9
3. -1
4. 10
5.
Find the domain of the composite function $f(g(x))$.

$f(x)= x+3$
$g(x)= 2/(x+6)$
1. $(-oo,3) uu (3,oo)$
2. $(-oo,oo)$
3. $(-oo,-6) uu (-6,3) uu (3,oo)$
4. $(-oo,-6) uu (-6,oo)$
6.
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. $(-oo,-2)$
7.
For x = -2, evaluate f(g(x)) - f(0), given that:

$f(x) = 2x + 5$
$g(x) = 4x$
1. -11
2. 6
3. -4
4. -16
8.
Given $f(x) = x+4, \ g(x) = x^2$ find $f(g(x-2))$.
1. $f(g(x-2))=x^2-4x+8$
2. $f(g(x-2))=x^2+x+2$
3. $f(g(x-2))=x+2$
4. $f(g(x-2))=x^2-4x+4$
9.
If $f(x)=3x-4$ and $f(g(x))=x$, then $g(x)$ is
1. $1/(3x-4)$
2. $(x+4)/3$
3. $3-4x$
4. $4x-3$
10.
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. $-1/(2(x^2 - 2))$
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