SOLUTION: If g(x)=1-x^2 and f(g(x))=(1-x^2)/x^2 when x does not equal 0, what is the value of f(1/2)?

Question 959132: If g(x)=1-x^2 and f(g(x))=(1-x^2)/x^2 when x does not equal 0, what is the value of f(1/2)?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
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 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 for . Adding to both sides we get:
x^2 + g(x) = 1
Subtracting g(x) from each side we get:
x^2 = 1 - g(x)

Now we express f(g(x)) in terms of g(x):

From this we can see where the input to f goes. Using this pattern for f(x) we get:

Now we can find f(1/2):

Simplifying...

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