For this case, we want to know what value of "x" makes:
[tex]g (x) = f (2)[/tex]
To find f (2), we substitute [tex]x = 2[/tex]in f (x).
[tex]f (x) = 3x-1\\f (2) = 3 (2) -1\\f (2) = 6-1\\f (2) = 5[/tex]
Now:
[tex]g (x) = f (2)\\g (x) = 5\\2x-3 = 5[/tex]
Adding 3 to both sides:
[tex]2x = 5 + 3\\2x = 8[/tex]
Dividing between 2 on both sides:
[tex]x = \frac {8} {2}\\x = 4\\Thus,\ x = 4\ makes\ g (x) = f (2)[/tex]
Answer:
[tex]x = 4[/tex]
