QuestionEvaluate the function $f(x)=\frac{3 x+8}{5 x-3}$ for: (a) $f(0)$ , (b) $f(1)$ , (c) $f(-1)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(7 x)$ , (h) $f(x+h)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{3 x+8}{5 x-3}$

STEP 2

To find $f(0)$ , we substitute $x=0$ into the function.
$f(0)=\frac{(0)+8}{5(0)-}$

STEP 3

Calculate the value of $f(0)$ .
$f(0)=\frac{-8}{3}$

STEP 4

To find $f(1)$ , we substitute $x=1$ into the function.
$f(1)=\frac{3(1)+8}{(1)-3}$

STEP 5

Calculate the value of $f(1)$ .
$f(1)=\frac{11}{2}$

STEP 6

To find $f(-1)$ , we substitute $x=-1$ into the function.
$f(-1)=\frac{3(-1)+8}{5(-1)-3}$

STEP 7

Calculate the value of $f(-1)$ .
$f(-1)=\frac{-5}{}$

STEP 8

To find $f(-x)$ , we substitute $-x$ into the function.
$f(-x)=\frac{3(-x)+8}{5(-x)-3}$

STEP 9

implify the expression for $f(-x)$ .
$f(-x)=\frac{-3x+8}{-5x-3}$

STEP 10

To find $-f(x)$ , we take the negative of the function.
$-f(x)=-\frac{3 x+8}{5 x-3}$

STEP 11

To find $f(x+)$ , we substitute $x+$ into the function.
$f(x+)=\frac{3(x+)+8}{5(x+)-3}$

STEP 12

implify the expression for $f(x+)$ .
$f(x+)=\frac{x+11}{5x+2}$

STEP 13

To find $f(7x)$ , we substitute $7x$ into the function.
$f(7x)=\frac{3(7x)+8}{5(7x)-3}$

STEP 14

implify the expression for $f(7x)$ .
$f(7x)=\frac{21x+8}{35x-3}$

STEP 15

To find $f(x+h)$ , we substitute $x+h$ into the function.
$f(x+h)=\frac{3(x+h)+8}{5(x+h)-3}$

STEP 16

implify the expression for $f(x+h)$ .
$f(x+h)=\frac{3x+3h+8}{5x+5h-3}$

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QuestionEvaluate the function $f(x)=\frac{3 x+8}{5 x-3}$ for: (a) $f(0)$ , (b) $f(1)$ , (c) $f(-1)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(7 x)$ , (h) $f(x+h)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{3 x+8}{5 x-3}$

STEP 2

To find $f(0)$ , we substitute $x=0$ into the function.
$f(0)=\frac{(0)+8}{5(0)-}$

STEP 3

Calculate the value of $f(0)$ .
$f(0)=\frac{-8}{3}$

STEP 4

To find $f(1)$ , we substitute $x=1$ into the function.
$f(1)=\frac{3(1)+8}{(1)-3}$

STEP 5

Calculate the value of $f(1)$ .
$f(1)=\frac{11}{2}$

STEP 6

To find $f(-1)$ , we substitute $x=-1$ into the function.
$f(-1)=\frac{3(-1)+8}{5(-1)-3}$

STEP 7

Calculate the value of $f(-1)$ .
$f(-1)=\frac{-5}{}$

STEP 8

To find $f(-x)$ , we substitute $-x$ into the function.
$f(-x)=\frac{3(-x)+8}{5(-x)-3}$

STEP 9

implify the expression for $f(-x)$ .
$f(-x)=\frac{-3x+8}{-5x-3}$

STEP 10

To find $-f(x)$ , we take the negative of the function.
$-f(x)=-\frac{3 x+8}{5 x-3}$

STEP 11

To find $f(x+)$ , we substitute $x+$ into the function.
$f(x+)=\frac{3(x+)+8}{5(x+)-3}$

STEP 12

implify the expression for $f(x+)$ .
$f(x+)=\frac{x+11}{5x+2}$

STEP 13

To find $f(7x)$ , we substitute $7x$ into the function.
$f(7x)=\frac{3(7x)+8}{5(7x)-3}$

STEP 14

implify the expression for $f(7x)$ .
$f(7x)=\frac{21x+8}{35x-3}$

STEP 15

To find $f(x+h)$ , we substitute $x+h$ into the function.
$f(x+h)=\frac{3(x+h)+8}{5(x+h)-3}$

STEP 16

implify the expression for $f(x+h)$ .
$f(x+h)=\frac{3x+3h+8}{5x+5h-3}$

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QuestionEvaluate the function f(x)=3x+85x−3f(x)=\frac{3 x+8}{5 x-3}f(x)=5x−33x+8​ for: (a) f(0)f(0)f(0), (b) f(1)f(1)f(1), (c) f(−1)f(-1)f(−1), (d) f(−x)f(-x)f(−x), (e) −f(x)-f(x)−f(x), (f) f(x+1)f(x+1)f(x+1), (g) f(7x)f(7 x)f(7x), (h) f(x+h)f(x+h)f(x+h).

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=3x+85x−3f(x)=\frac{3 x+8}{5 x-3}f(x)=5x−33x+8​

STEP 2

To find f(0)f(0)f(0), we substitute x=0x=0x=0 into the function.f(0)=(0)+85(0)−f(0)=\frac{(0)+8}{5(0)-}f(0)=5(0)−(0)+8​

STEP 3

Calculate the value of f(0)f(0)f(0).f(0)=−83f(0)=\frac{-8}{3}f(0)=3−8​

STEP 4

To find f(1)f(1)f(1), we substitute x=1x=1x=1 into the function.f(1)=3(1)+8(1)−3f(1)=\frac{3(1)+8}{(1)-3}f(1)=(1)−33(1)+8​

STEP 5

Calculate the value of f(1)f(1)f(1).f(1)=112f(1)=\frac{11}{2}f(1)=211​

STEP 6

To find f(−1)f(-1)f(−1), we substitute x=−1x=-1x=−1 into the function.f(−1)=3(−1)+85(−1)−3f(-1)=\frac{3(-1)+8}{5(-1)-3}f(−1)=5(−1)−33(−1)+8​

STEP 7

Calculate the value of f(−1)f(-1)f(−1).f(−1)=−5f(-1)=\frac{-5}{}f(−1)=−5​

STEP 8

To find f(−x)f(-x)f(−x), we substitute −x-x−x into the function.f(−x)=3(−x)+85(−x)−3f(-x)=\frac{3(-x)+8}{5(-x)-3}f(−x)=5(−x)−33(−x)+8​

STEP 9

implify the expression for f(−x)f(-x)f(−x).f(−x)=−3x+8−5x−3f(-x)=\frac{-3x+8}{-5x-3}f(−x)=−5x−3−3x+8​

STEP 10

To find −f(x)-f(x)−f(x), we take the negative of the function.−f(x)=−3x+85x−3-f(x)=-\frac{3 x+8}{5 x-3}−f(x)=−5x−33x+8​

STEP 11

To find f(x+)f(x+)f(x+), we substitute x+x+x+ into the function.f(x+)=3(x+)+85(x+)−3f(x+)=\frac{3(x+)+8}{5(x+)-3}f(x+)=5(x+)−33(x+)+8​

STEP 12

implify the expression for f(x+)f(x+)f(x+).f(x+)=x+115x+2f(x+)=\frac{x+11}{5x+2}f(x+)=5x+2x+11​

STEP 13

To find f(7x)f(7x)f(7x), we substitute 7x7x7x into the function.f(7x)=3(7x)+85(7x)−3f(7x)=\frac{3(7x)+8}{5(7x)-3}f(7x)=5(7x)−33(7x)+8​

STEP 14

implify the expression for f(7x)f(7x)f(7x).f(7x)=21x+835x−3f(7x)=\frac{21x+8}{35x-3}f(7x)=35x−321x+8​

STEP 15

To find f(x+h)f(x+h)f(x+h), we substitute x+hx+hx+h into the function.f(x+h)=3(x+h)+85(x+h)−3f(x+h)=\frac{3(x+h)+8}{5(x+h)-3}f(x+h)=5(x+h)−33(x+h)+8​

STEP 16

implify the expression for f(x+h)f(x+h)f(x+h).f(x+h)=3x+3h+85x+5h−3f(x+h)=\frac{3x+3h+8}{5x+5h-3}f(x+h)=5x+5h−33x+3h+8​

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QuestionEvaluate the function $f(x)=\frac{3 x+8}{5 x-3}$ for: (a) $f(0)$ , (b) $f(1)$ , (c) $f(-1)$ , (d) $f(-x)$ , (e) $-f(x)$ , (f) $f(x+1)$ , (g) $f(7 x)$ , (h) $f(x+h)$ .

Assumptions1. The function is $f(x)=\frac{3 x+8}{5 x-3}$

To find $f(0)$ , we substitute $x=0$ into the function.
$f(0)=\frac{(0)+8}{5(0)-}$

Calculate the value of $f(0)$ .
$f(0)=\frac{-8}{3}$

To find $f(1)$ , we substitute $x=1$ into the function.
$f(1)=\frac{3(1)+8}{(1)-3}$

Calculate the value of $f(1)$ .
$f(1)=\frac{11}{2}$

To find $f(-1)$ , we substitute $x=-1$ into the function.
$f(-1)=\frac{3(-1)+8}{5(-1)-3}$

Calculate the value of $f(-1)$ .
$f(-1)=\frac{-5}{}$

To find $f(-x)$ , we substitute $-x$ into the function.
$f(-x)=\frac{3(-x)+8}{5(-x)-3}$

implify the expression for $f(-x)$ .
$f(-x)=\frac{-3x+8}{-5x-3}$

To find $-f(x)$ , we take the negative of the function.
$-f(x)=-\frac{3 x+8}{5 x-3}$

To find $f(x+)$ , we substitute $x+$ into the function.
$f(x+)=\frac{3(x+)+8}{5(x+)-3}$

implify the expression for $f(x+)$ .
$f(x+)=\frac{x+11}{5x+2}$

To find $f(7x)$ , we substitute $7x$ into the function.
$f(7x)=\frac{3(7x)+8}{5(7x)-3}$

implify the expression for $f(7x)$ .
$f(7x)=\frac{21x+8}{35x-3}$

To find $f(x+h)$ , we substitute $x+h$ into the function.
$f(x+h)=\frac{3(x+h)+8}{5(x+h)-3}$

implify the expression for $f(x+h)$ .
$f(x+h)=\frac{3x+3h+8}{5x+5h-3}$