SOLUTION: f(x) = (1 + x)/x g(x) = 1/(1 - x) h(x) = 1/(1 + x) If so, (g o h)(x) = a. x b. 2 - x c. -x d. x/(2x + 1) e. (1 - x)/(2 - x) f. (1 + x)/x g. (2 - x)/(1 - x)

Algebra ->  Expressions -> SOLUTION: f(x) = (1 + x)/x g(x) = 1/(1 - x) h(x) = 1/(1 + x) If so, (g o h)(x) = a. x b. 2 - x c. -x d. x/(2x + 1) e. (1 - x)/(2 - x) f. (1 + x)/x g. (2 - x)/(1 - x)       Log On


   

Question 50554: f(x) = (1 + x)/x
g(x) = 1/(1 - x)
h(x) = 1/(1 + x)
If so, (g o h)(x) =
a. x
b. 2 - x
c. -x
d. x/(2x + 1)
e. (1 - x)/(2 - x)
f. (1 + x)/x
g. (2 - x)/(1 - x)
h. (1 - x)/x
i. 2 + x
j. none of these
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
g(x) = 1/(1 - x)
h(x) = 1/(1 + x)


(g o h)(x) = g[ f(x) ]
g[ f(x) ] = 1%2F%281-%281%2F%281%2Bx%29%29%29+

This looks a LOT worse than it really is!! It's a complex fraction, and I have a LOT of these worked out on my Math in Living Color pages of my website! I'm more comfortable in that format, and they are in "Living Color"!

Multiply both numerator and denominator by the LCD which is (1+x).
g[ f(x) ] = %28%281%2Bx%29%2F%281%2Bx%29%29%2A%281%2F%281-%281%2F%281%2Bx%29%29%29%29+
g[ f(x) ] = +%28+%281%2Bx%29+%29+%2F+%28%281%2Bx%29-%281%2Bx%29%2A%28%281%2F%281%2Bx%29%29%29%29+
g[ f(x) ] = +%28+%281%2Bx%29+%29+%2F+%28%281%2Bx%29-1%29%29+
g[ f(x) ] = +%28%28+1%2Bx%29+%29+%2F+x, which is the f) answer.

R^2 at SCC