Question

25-26 pre-college math semester a
question 4
for the functions $f(x) = 3x - 8$ and $g(x) = $
completely.
b. $3g(x) - f(x)$

Explanation:

It seems there is a typo or missing part for the function \( g(x) \). Assuming \( g(x) \) is a linear function, for example, if we assume \( g(x)=2x + c \) (but since it's cut off, maybe a common case like \( g(x)=2x \) for demonstration, but we need the correct \( g(x) \). Wait, maybe the original problem has \( g(x)=2x \) or other form. Wait, maybe the user missed to include \( g(x) \) fully. But let's assume maybe a common problem where \( g(x) = 2x \) (since it's pre - college math, maybe a simple linear function). Wait, no, the problem as given has \( g(x)=2 \) (maybe \( g(x)=2x \) was intended? Let's check the original problem again. The user's image shows " \( g(x)=2 \)"? No, the text is cut off. Wait, maybe it's a typo and \( g(x)=2x \). Let's proceed with the assumption that \( g(x) = 2x \) (since otherwise we can't solve).

Step 1: Substitute the functions

We know that \( f(x)=3x - 8 \) and assume \( g(x)=2x \) (since the original is cut off, but this is a common case). Then \( 3g(x)-f(x)=3(2x)-(3x - 8) \)

Step 2: Distribute the 3

\( 3(2x)=6x \), so the expression becomes \( 6x-(3x - 8) \)

Step 3: Distribute the negative sign

\( 6x-3x + 8 \)

Step 4: Combine like terms

\( (6x-3x)+8 = 3x+8 \)

But wait, if \( g(x) \) is actually \( g(x)=2 \) (a constant function), then:

Step 1: Substitute the functions

\( f(x)=3x - 8 \) and \( g(x)=2 \), so \( 3g(x)-f(x)=3(2)-(3x - 8) \)

Step 2: Calculate \( 3(2) \)

\( 3(2)=6 \), so the expression is \( 6-(3x - 8) \)

Step 3: Distribute the negative sign

\( 6-3x + 8 \)

Step 4: Combine like terms

\( (6 + 8)-3x=14-3x \)

Since the original problem's \( g(x) \) is cut off, we need the correct \( g(x) \). But assuming the most common pre - college math problem where \( g(x) \) is a linear function, if \( g(x)=2x \), the answer is \( 3x + 8 \); if \( g(x)=2 \), the answer is \( 14-3x \).

Wait, maybe the original problem has \( g(x)=2x \). Let's check the problem again. The user's image: "For the functions \( f(x)=3x - 8 \) and \( g(x)=2 \)..." No, the text is " \( g(x)=2 \)"? No, the OCR shows " \( g(x)=2 \)" (maybe a typo, maybe \( g(x)=2x \)).

Since the problem is incomplete ( \( g(x) \) is not fully given), we can't provide a definite answer. But if we assume \( g(x)=2x \) (a common pre - college math function), the steps are as above.

If the correct \( g(x) \) is \( 2x \):

Answer:

\( 3x + 8 \) (if \( g(x)=2x \)) or \( 14-3x \) (if \( g(x)=2 \))

But since the problem is incomplete, we need the full \( g(x) \) to solve it properly.