Certainly! Let's solve the problem step-by-step.
We are given two functions:
[tex]\[ f(x) = 3x - 1 \][/tex]
[tex]\[ g(x) = 2x - 3 \][/tex]
We need to find a value of [tex]\( x \)[/tex] such that:
[tex]\[ g(x) = f(2) \][/tex]
Let's start by evaluating [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 3(2) - 1 \][/tex]
[tex]\[ f(2) = 6 - 1 \][/tex]
[tex]\[ f(2) = 5 \][/tex]
Now, we need to find the value of [tex]\( x \)[/tex] for which:
[tex]\[ g(x) = 5 \][/tex]
Substitute [tex]\( 5 \)[/tex] into the [tex]\( g(x) \)[/tex] function:
[tex]\[ 2x - 3 = 5 \][/tex]
To solve for [tex]\( x \)[/tex], add 3 to both sides of the equation:
[tex]\[ 2x - 3 + 3 = 5 + 3 \][/tex]
[tex]\[ 2x = 8 \][/tex]
Now, divide both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{8}{2} \][/tex]
[tex]\[ x = 4 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( g(x) = f(2) \)[/tex] is:
[tex]\[ \boxed{4} \][/tex]
