Question

1. $g(x) = 5x$
2. $g(x) = x + 4$

Explanation:

Since the problem is not specified (e.g., finding the inverse, evaluating at a point, graphing), I'll assume a common task like finding the inverse function. Let's solve for the inverse of both functions.

For \( g(x) = 5x \) (Problem 4)

Step 1: Replace \( g(x) \) with \( y \)

\( y = 5x \)

Step 2: Swap \( x \) and \( y \)

\( x = 5y \)

Step 3: Solve for \( y \)

Divide both sides by 5: \( y = \frac{x}{5} \)

Step 4: Replace \( y \) with \( g^{-1}(x) \)

\( g^{-1}(x) = \frac{x}{5} \)

For \( g(x) = x + 4 \) (Problem 6)

Step 1: Replace \( g(x) \) with \( y \)

\( y = x + 4 \)

Step 2: Swap \( x \) and \( y \)

\( x = y + 4 \)

Step 3: Solve for \( y \)

Subtract 4 from both sides: \( y = x - 4 \)

Step 4: Replace \( y \) with \( g^{-1}(x) \)

\( g^{-1}(x) = x - 4 \)

Answer:

s:

• For \( g(x) = 5x \), the inverse is \( \boldsymbol{g^{-1}(x) = \frac{x}{5}} \)
• For \( g(x) = x + 4 \), the inverse is \( \boldsymbol{g^{-1}(x) = x - 4} \)