SOLUTION: If f(x)= x-1 over x+2 and f(g(x))= 1/x, then which of the following could be g(x)? A. 2+x over x-1 B. x+2 over x-1 C. (x+1)(x+2) D. x-2 over x-1

Algebra ->  Finance -> SOLUTION: If f(x)= x-1 over x+2 and f(g(x))= 1/x, then which of the following could be g(x)? A. 2+x over x-1 B. x+2 over x-1 C. (x+1)(x+2) D. x-2 over x-1      Log On


   

Question 1088764: If f(x)= x-1 over x+2 and f(g(x))= 1/x, then which of the following could be g(x)?
A. 2+x over x-1
B. x+2 over x-1
C. (x+1)(x+2)
D. x-2 over x-1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=+%28x-1%29+%2F%28x%2B2%29 and f%28g%28x%29%29=+1%2Fx
let say g%28x%29=a
then
f%28g%28x%29%29=+%28a-1%29+%2F%28a%2B2%29
if f%28g%28x%29%29=+1%2Fx, we have"
1%2Fx=+%28a-1%29+%2F%28a%2B2%29.......solve for a
a%2B2=+x%28a-1%29+
a%2B2=+xa-x+
x%2B2=+xa-a
x%2B2=+%28x-1%29a
a=%28x%2B2%29%2F%28x-1%29
so, g%28x%29=%28x%2B2%29%2F%28x-1%29

check:






f%28g%28x%29%29=+%282%2B1+%29%2F%28x%2B2x%29
f%28g%28x%29%29=+3%2F3x
f%28g%28x%29%29=+1%2Fx