SOLUTION: let g(x) = 1/x^2 and h(x)= 1/((sqrt x )- 1) please determine the the following function h(g(x))

Algebra ->  Functions -> SOLUTION: let g(x) = 1/x^2 and h(x)= 1/((sqrt x )- 1) please determine the the following function h(g(x))       Log On


   

Question 316056: let g(x) = 1/x^2 and h(x)= 1/((sqrt x )- 1)
please determine the the following function
h(g(x))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
h%28x%29=1%2F%28sqrt%28x%29-1%29 Start with the second function.


h%28g%28x%29%29=1%2F%28sqrt%281%2F%28x%5E2%29%29-1%29 Plug in g%28x%29=1%2F%28x%5E2%29


h%28g%28x%29%29=1%2F%28sqrt%281%29%2Fsqrt%28x%5E2%29-1%29 Break up the square root.


h%28g%28x%29%29=1%2F%281%2Fsqrt%28x%5E2%29-1%29 Take the square root of 1 to get 1.


h%28g%28x%29%29=1%2F%281%2Fx-1%29 Take the square root of x%5E2 to get 'x' (this is assuming that 'x' is non-negative)


h%28g%28x%29%29=1%2F%281%2Fx-x%2Fx%29 Rewrite the second '1' as x%2Fx


h%28g%28x%29%29=1%2F%28%281-x%29%2Fx%29 Combine the lower fractions.


h%28g%28x%29%29=x%2F%281-x%29 Take the reciprocal of the lower fraction.


So the composite function is h%28g%28x%29%29=x%2F%281-x%29