Question:
Given f(x) = 3x-1 and g(x)=2x-3, for which value of x does g(x) = f(2)?
Answer:
The value of x is 4 for g(x) = f(2)
Solution:
Given that,
[tex]f(x) = 3x-1\\\\g(x) = 2x - 3[/tex]
We have to find the value of "x" such that g(x) = f(2)
Let us first find f(2)
Substitute x = 2 in f(x) function
[tex]f(x) = 3x-1\\\\f(2) = 3(2) - 1\\\\f(2) = 6 - 1 = 5[/tex]
Thus f(2) is 5
Now find: g(x) = f(2)
Equate given function of g(x) and f(2) which is found to be 5
[tex]g(x) = f(2)\\\\2x - 3 = 5\\\\\text{Move the constants to other side }\\\\2x = 5 + 3\\\\2x = 8\\\\\text{Divide both sides of equation by 4 }\\\\x = 4[/tex]
Thus for x = 4 , we get g(x) = f(2)
