Question

4.5 more practice hw
evaluate each function.

1. $g(x) = 2x - 4$; find $g(-2)$
2. $h(n) = -n + 5$; find $h(-7)$
3. $p(a) = a^2 + 2$; find $p(-9)$
4. $p(x) = x^3 + 3x$; find $p(-3)$

perform the indicated operation.

1. $f(x) = x + 5$

$g(x) = 2x + 3$
find $(f + g)(x)$

1. $g(x) = 2x - 3$

$f(x) = x^3 - 2x$
find $(g + f)(x)$

1. $g(x) = 4x + 2$

$h(x) = x^2 + 5$
find $(g - h)(x)$

1. $g(t) = 4t$

$h(t) = 4t + 4$
find $(g - h)(t)$

Explanation:

Step1: Substitute $x=-2$ into $g(x)$

$g(-2)=2(-2)-4$

Step2: Calculate the result

$g(-2)=-4-4=-8$

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Step1: Substitute $n=-7$ into $h(n)$

$h(-7)=-(-7)+5$

Step2: Calculate the result

$h(-7)=7+5=12$

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Step1: Substitute $a=-9$ into $p(a)$

$p(-9)=(-9)^2+2$

Step2: Calculate the result

$p(-9)=81+2=83$

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Step1: Substitute $x=-3$ into $p(x)$

$p(-3)=(-3)^3+3(-3)$

Step2: Calculate the result

$p(-3)=-27-9=-36$

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Step1: Define $(f+g)(x)$ as $f(x)+g(x)$

$(f+g)(x)=(x+5)+(2x+3)$

Step2: Combine like terms

$(f+g)(x)=x+2x+5+3=3x+8$

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Step1: Define $(g+f)(x)$ as $g(x)+f(x)$

$(g+f)(x)=(2x-3)+(x^3-2x)$

Step2: Combine like terms

$(g+f)(x)=x^3+2x-2x-3=x^3-3$

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Step1: Define $(g-h)(x)$ as $g(x)-h(x)$

$(g-h)(x)=(4x+2)-(x^2+5)$

Step2: Distribute and combine terms

$(g-h)(x)=-x^2+4x+2-5=-x^2+4x-3$

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Step1: Define $(g-h)(t)$ as $g(t)-h(t)$

$(g-h)(t)=(4t)-(4t+4)$

Step2: Distribute and combine terms

$(g-h)(t)=4t-4t-4=-4$

Answer:

1. $g(-2)=-8$
2. $h(-7)=12$
3. $p(-9)=83$
4. $p(-3)=-36$
5. $(f+g)(x)=3x+8$
6. $(g+f)(x)=x^3-3$
7. $(g-h)(x)=-x^2+4x-3$
8. $(g-h)(t)=-4$