Question

Given f(x) =3x-1 and g(x)=2x-3, for which value of x does g(x) =f(2)?

Answer 1

g(x) = f(2)

2x - 3 = 3*2 - 1

2x - 3 = 5

2x = 8

x = 4

Answer 2

For this case, we want to know what value of "x" makes:

`g (x) = f (2)`

To find f (2), we substitute
`x = 2`in f (x).

`f (x) = 3x-1\\f (2) = 3 (2) -1\\f (2) = 6-1\\f (2) = 5`

Now:

`g (x) = f (2)\\g (x) = 5\\2x-3 = 5`

Adding 3 to both sides:

`2x = 5 + 3\\2x = 8`

Dividing between 2 on both sides:

`x = \frac {8} {2}\\x = 4\\Thus,\ x = 4\ makes\ g (x) = f (2)`

Answer:

`x = 4`