SOLUTION: Help Please Thanks. Given f(x)=x^2/2, g(x)=2/x, and h(x)=4x-3, find h(f(g(x))). A. 2/x^2 B. 16-48x+9x^2 C. 8-3x^2/x^2 D. 16-4x^2/x^4

Algebra ->  Functions -> SOLUTION: Help Please Thanks. Given f(x)=x^2/2, g(x)=2/x, and h(x)=4x-3, find h(f(g(x))). A. 2/x^2 B. 16-48x+9x^2 C. 8-3x^2/x^2 D. 16-4x^2/x^4      Log On


   

Question 996339: Help Please Thanks.
Given f(x)=x^2/2, g(x)=2/x, and h(x)=4x-3, find h(f(g(x))).
A. 2/x^2
B. 16-48x+9x^2
C. 8-3x^2/x^2
D. 16-4x^2/x^4
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

h%28f%28g%28x%29%29%29=+h%28f%282%2Fx%29%29......since f%28g%28x%29%29=f%282%2Fx%29=%282%2Fx%29%5E2%2F2=%284%2Fx%5E2%29%2F2=4%2F2x%5E2=2%2Fx%5E2 we have
h%28f%28g%28x%29%29%29=+h%282%2Fx%5E2%29....given h%28x%29=4x-3, substitute x with %282%2Fx%5E2%29
h%28f%28g%28x%29%29%29=+4%282%2Fx%5E2%29-3
h%28f%28g%28x%29%29%29=+8%2Fx%5E2-3
h%28f%28g%28x%29%29%29=+8%2Fx%5E2-3x%5E2%2Fx%5E2
h%28f%28g%28x%29%29%29=+%288-3x%5E2%29%2Fx%5E2
so, your answer is C