Question

given $f(x) = 3x - 1$ and $g(x) = 2x - 3$, for which value of $x$ does $g(x) = f(2)$?
$\bigcirc$ $x = \dfrac{3}{2}$
$\bigcirc$ $x = 2$
$\bigcirc$ $x = \dfrac{5}{2}$
$\bigcirc$ $x = 4$

Explanation:

Step1: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x)=3x - 1 \). So \( f(2)=3\times2 - 1=6 - 1 = 5 \).

Step2: Solve \( g(x)=f(2) \)

We know \( g(x)=2x - 3 \) and \( f(2) = 5 \), so set \( 2x - 3=5 \). Add 3 to both sides: \( 2x=5 + 3=8 \). Then divide by 2: \( x=\frac{8}{2}=4 \)? Wait, no, wait. Wait, \( f(2)=32 - 1 = 5 \). Then \( g(x)=2x - 3 = 5 \). So \( 2x=5 + 3=8 \), \( x = 4 \)? Wait, but let's check again. Wait, maybe I made a mistake. Wait, \( f(2)=32 -1=5 \). Then \( g(x)=2x -3=5 \). So \( 2x=8 \), \( x=4 \). But let's check the options. Option D is \( x = 4 \). Wait, but let's re - check. Wait, maybe I miscalculated \( f(2) \). \( f(x)=3x -1 \), \( x = 2 \), so \( 3*2=6 \), \( 6 -1=5 \). Then \( g(x)=2x -3=5 \). So \( 2x=5 + 3=8 \), \( x = 4 \). So the answer is \( x = 4 \).

Answer:

\( x = 4 \) (corresponding to the option \( x = 4 \))