Solved on Dec 07, 2023

Find the value of $\frac{x-5}{8x+2}$ when $x=2$ , and simplify the result.

STEP 1

Assumptions
1. The function $f$ is defined by $f(x)=\frac{x-5}{8x+2}$ .
2. We need to find the value of $f(2)$ .

STEP 2

To find $f(2)$ , we need to substitute $x$ with $2$ in the function $f(x)$ .
$f(2)=\frac{2-5}{8 \cdot 2+2}$

STEP 3

Perform the subtraction in the numerator and the multiplication and addition in the denominator.
$f(2)=\frac{-3}{16+2}$

STEP 4

Add the numbers in the denominator.
$f(2)=\frac{-3}{18}$

STEP 5

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ in this case.
$f(2)=\frac{-3/3}{18/3}$

STEP 6

Perform the division.
$f(2)=\frac{-1}{6}$
The simplified value of $f(2)$ is $-\frac{1}{6}$ .

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Find the value of $\frac{x-5}{8x+2}$ when $x=2$ , and simplify the result.

STEP 1

Assumptions
1. The function $f$ is defined by $f(x)=\frac{x-5}{8x+2}$ .
2. We need to find the value of $f(2)$ .

STEP 2

To find $f(2)$ , we need to substitute $x$ with $2$ in the function $f(x)$ .
$f(2)=\frac{2-5}{8 \cdot 2+2}$

STEP 3

Perform the subtraction in the numerator and the multiplication and addition in the denominator.
$f(2)=\frac{-3}{16+2}$

STEP 4

Add the numbers in the denominator.
$f(2)=\frac{-3}{18}$

STEP 5

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ in this case.
$f(2)=\frac{-3/3}{18/3}$

STEP 6

Perform the division.
$f(2)=\frac{-1}{6}$
The simplified value of $f(2)$ is $-\frac{1}{6}$ .

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Find the value of x−58x+2\frac{x-5}{8x+2}8x+2x−5​ when x=2x=2x=2, and simplify the result.

STEP 1

Assumptions1. The function fff is defined by f(x)=x−58x+2f(x)=\frac{x-5}{8x+2}f(x)=8x+2x−5​.2. We need to find the value of f(2)f(2)f(2).

STEP 2

To find f(2)f(2)f(2), we need to substitute xxx with 222 in the function f(x)f(x)f(x).f(2)=2−58⋅2+2f(2)=\frac{2-5}{8 \cdot 2+2}f(2)=8⋅2+22−5​

STEP 3

Perform the subtraction in the numerator and the multiplication and addition in the denominator.f(2)=−316+2f(2)=\frac{-3}{16+2}f(2)=16+2−3​

STEP 4

Add the numbers in the denominator.f(2)=−318f(2)=\frac{-3}{18}f(2)=18−3​

STEP 5

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 333 in this case.f(2)=−3/318/3f(2)=\frac{-3/3}{18/3}f(2)=18/3−3/3​

STEP 6

Perform the division.f(2)=−16f(2)=\frac{-1}{6}f(2)=6−1​The simplified value of f(2)f(2)f(2) is −16-\frac{1}{6}−61​.

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Find the value of $\frac{x-5}{8x+2}$ when $x=2$ , and simplify the result.

Assumptions
1. The function $f$ is defined by $f(x)=\frac{x-5}{8x+2}$ .
2. We need to find the value of $f(2)$ .

To find $f(2)$ , we need to substitute $x$ with $2$ in the function $f(x)$ .
$f(2)=\frac{2-5}{8 \cdot 2+2}$

Perform the subtraction in the numerator and the multiplication and addition in the denominator.
$f(2)=\frac{-3}{16+2}$

Add the numbers in the denominator.
$f(2)=\frac{-3}{18}$

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ in this case.
$f(2)=\frac{-3/3}{18/3}$

Perform the division.
$f(2)=\frac{-1}{6}$
The simplified value of $f(2)$ is $-\frac{1}{6}$ .