function $$ g $$ is defined as follows. $$ g(x)=\frac{4 x}{2 x-17} $$ $$ g(6) $$. mplify your answer as much as possible. If applicable, click on "Undefined"

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UpStudy AI · Accepted Answer

Evaluate the expression by following steps:
- step0: Evaluate:
  $$\frac{4x}{2x-17}$$
- step1: Substitute:
  $$\frac{4\times 6}{2\times 6-17}$$
- step2: Multiply the numbers:
  $$\frac{4\times 6}{12-17}$$
- step3: Multiply the numbers:
  $$\frac{24}{12-17}$$
- step4: Subtract the numbers:
  $$\frac{24}{-5}$$
- step5: Rewrite the fraction:
  $$-\frac{24}{5}$$
To find $$ g(6) $$ for the function $$ g(x) = \frac{4x}{2x - 17} $$, we substitute $$ x = 6 $$ into the function:

$$
g(6) = \frac{4 \cdot 6}{2 \cdot 6 - 17}
$$

Calculating the numerator:

$$
4 \cdot 6 = 24
$$

Calculating the denominator:

$$
2 \cdot 6 - 17 = 12 - 17 = -5
$$

Now substituting these values back into the function:

$$
g(6) = \frac{24}{-5} = -\frac{24}{5}
$$

Thus, the simplified answer is:

$$
g(6) = -\frac{24}{5}
$$

This can also be expressed as:

$$
g(6) = -4\frac{4}{5} \quad \text{or} \quad g(6) = -4.8
$$

The most appropriate result format is:

$$
g(6) = -\frac{24}{5}
$$
$$ g(6) = -\frac{24}{5} $$

function \( g \) is defined as follows. \( g(x)=\frac{4 x}{2 x-17} \) \( g(6) \). mplify your answer as much as possible. If applicable, click on "Undefined"

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