Question 959132
One way to solve this is to find f(x) first and then use that for find f(1/2).

To find f(x) from f(g(x)) we look to express {{{(1-x^2)/x^2}}} in terms of g(x). The numerator of f(g(x)) is already equal to g(x). For the denomoinator, x^2, we need to solve {{{g(x) = 1-x^2}}} for {{{x^2}}}. Adding {{{x^2}}} to both sides we get:
x^2 + g(x) = 1
Subtracting g(x) from each side we get:
x^2 = 1 - g(x)<br>
Now we express f(g(x)) in terms of g(x):
{{{f(g(x)) = g(x)/(1-g(x))}}}
From this we can see where the input to f goes. Using this pattern for f(x) we get:
{{{f(x) = x/(1-x)}}}<br>
Now we can find f(1/2):
{{{f(1/2) = (1/2)/(1-(1/2))}}}
Simplifying...
{{{f(1/2) = (1/2)/(1/2)}}}
{{{f(1/2) = 1}}}