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QuestionEvaluate the following functions at x=3x=3: f(x)=x−3f(x)=x-3, g(x)=x2−3x+5g(x)=x^{2}-3x+5, h(x)=x3+x+33h(x)=\sqrt[3]{x^{3}+x+3}, p(x)=x2+1x+4p(x)=\frac{x^{2}+1}{x+4}, f(x)=∣x−5∣f(x)=|x-5|. Also, for f(x)=x+8f(x)=x+8, find f(4)f(4), f(−2)f(-2), f(−x)f(-x), f(x+3)f(x+3), and f(x2+x+1)f\left(x^{2}+x+1\right).

Studdy Solution

STEP 1

Assumptions1. The variable xx is a real number. . The functions are defined for the given values of xx.

STEP 2

Evaluate the function f(x)=x−f(x)=x- at x=x=.
f()=−f()=-

STEP 3

Calculate the value of f(3)f(3).
f(3)=3−3=0f(3)=3-3=0

STEP 4

Evaluate the function g(x)=x2−3x+g(x)=x^{2}-3x+ at x=3x=3.
g(3)=32−3(3)+g(3)=3^{2}-3(3)+

STEP 5

Calculate the value of g(3)g(3).
g(3)=32−3(3)+5=9−9+5=5g(3)=3^{2}-3(3)+5=9-9+5=5

STEP 6

Evaluate the function h(x)=x3+x+33h(x)=\sqrt[3]{x^{3}+x+3} at x=3x=3.
h(3)=33+3+33h(3)=\sqrt[3]{3^{3}+3+3}

STEP 7

Calculate the value of h(3)h(3).
h(3)=33+3+33=27+3+33=333h(3)=\sqrt[3]{3^{3}+3+3}=\sqrt[3]{27+3+3}=\sqrt[3]{33}

STEP 8

Evaluate the function p(x)=x2+1x+4p(x)=\frac{x^{2}+1}{x+4} at x=3x=3.
p(3)=32+13+4p(3)=\frac{3^{2}+1}{3+4}

STEP 9

Calculate the value of p(3)p(3).
p(3)=32+3+4=9+7=7p(3)=\frac{3^{2}+}{3+4}=\frac{9+}{7}=\frac{}{7}

STEP 10

Evaluate the function f(x)=∣x−5∣f(x)=|x-5| at x=3x=3.
f(3)=∣3−5∣f(3)=|3-5|

STEP 11

Calculate the value of f(3)f(3).
f(3)=∣3−5∣=∣−∣=f(3)=|3-5|=|-|=

STEP 12

Evaluate the function f(x)=x+8f(x)=x+8 at x=4x=4.
f(4)=4+8f(4)=4+8

STEP 13

Calculate the value of f()f().
f()=+8=12f()=+8=12

STEP 14

Evaluate the function f(x)=x+8f(x)=x+8 at x=−2x=-2.
f(−2)=−2+8f(-2)=-2+8

STEP 15

Calculate the value of f(−2)f(-2).
f(−2)=−2+8=f(-2)=-2+8=

STEP 16

Evaluate the function f(x)=x+8f(x)=x+8 at x=−xx=-x.
f(−x)=−x+8f(-x)=-x+8

STEP 17

Evaluate the function f(x)=x+f(x)=x+ at x=x+3x=x+3.
f(x+3)=(x+3)+f(x+3)=(x+3)+

STEP 18

implify the expression for f(x+3)f(x+3).
f(x+3)=x+11f(x+3)=x+11

STEP 19

Evaluate the function f(x)=x+8f(x)=x+8 at x=x+x+1x=x^{}+x+1.
f(x+x+1)=(x+x+1)+8f\left(x^{}+x+1\right)=(x^{}+x+1)+8

STEP 20

implify the expression for f(x+x+)f\left(x^{}+x+\right).
f(x+x+)=x+x+9f\left(x^{}+x+\right)=x^{}+x+9The answers are. f(3)=0f(3)=0 . g(3)=5g(3)=5
3. h(3)=333h(3)=\sqrt[3]{33}
4. p(3)=107p(3)=\frac{10}{7}
5. f(3)=f(3)=
6. f(4)=12f(4)=12
7. f(−)=6f(-)=6
8. f(−x)=−x+8f(-x)=-x+8
9. f(x+3)=x+11f(x+3)=x+11
10. f(x+x+)=x+x+9f\left(x^{}+x+\right)=x^{}+x+9

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