We are given two functions:

• $f(x) = x - 2$
• $g(x) = 2x - 6$

We need to evaluate the expression $\frac{g(4)}{f(3)}$.

Step 1: Evaluate $g(4)$

Substitute $x = 4$ into the function $g(x)$:

$g(4) = 2(4) - 6 = 8 - 6 = 2$

Step 2: Evaluate $f(3)$

Substitute $x = 3$ into the function $f(x)$:

$f(3) = 3 - 2 = 1$

Step 3: Compute $\frac{g(4)}{f(3)}$

Now, substitute the values of $g(4)$ and $f(3)$:

$\frac{g(4)}{f(3)} = \frac{2}{1} = 2$

Final Answer:

$\frac{g(4)}{f(3)} = 2$

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Would you like more details on this or have any questions? Here are 5 related questions:

1. What is the general process to evaluate a composite function?
2. How would the result change if the functions were squared or cubed?
3. What happens if the function involves higher-order polynomials?
4. How do you find the inverse of a linear function like $f(x)$?
5. How can you graph the functions $f(x)$ and $g(x)$ based on their equations?

Tip: When evaluating functions at specific values, always ensure that the input is substituted correctly and simplify the expressions step by step.