SOLUTION: If g(x)=2x-4 and f is the function defined such f(g(x))=x, then f(x)= A) -2x+4 B) x-2 C) {{{(-1/2)x-2}}} D) {{{(1/2)x+2}}}

Algebra ->  Expressions -> SOLUTION: If g(x)=2x-4 and f is the function defined such f(g(x))=x, then f(x)= A) -2x+4 B) x-2 C) {{{(-1/2)x-2}}} D) {{{(1/2)x+2}}}      Log On


   

Question 1042050: If g(x)=2x-4 and f is the function defined such f(g(x))=x, then f(x)=
A) -2x+4
B) x-2
C) %28-1%2F2%29x-2
D) %281%2F2%29x%2B2
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
g(x)=2x-4 and f is the function defined such f(g(x))=x, then f(x)=
Let     f(x) ≡ Ax+B

Then f(g(x)) ≡ A(2x-4)+B ≡ 2Ax-4A+B

    2Ax-4A+B ≡ x

Therefore equating coefficients of x: 

       2A = 1
        A = 1/2

Equating constant terms:

    -4A+B = 0
-4(1/2)+B = 0
     -2+B = 0
        B = 2

Therefore f(x) ≡ Ax+B ≡ (1/2)x+2

Edwin