SOLUTION: let f(x)=1+1/x^2, find a function y=g(x) so that f(g(x))=x

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Question 1015265: let f(x)=1+1/x^2, find a function y=g(x) so that f(g(x))=x
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
let f%28x%29=1%2B1%2Fx%5E2, find a function y=g%28x%29 so that f%28g%28x%29%5E%22%22%29=x

Substitute y for x in the right side of f(x) and set it equal to x,
and solve for y:

1%2B1%2Fy%5E2%22%22=%22%22x

1%2Fy%5E2%22%22=%22%22x-1

Take reciprocals of both sides:

y%5E2%22%22=%22%221%2F%28x-1%29

Take positive square roots of both sides:

y%22%22=%22%22g%28x%29%22%22=%22%221%2Fsqrt%28x-1%29

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Checking to see if f%28g%28x%29%5E%22%22%29=x:

f%28g%28x%29%5E%22%22%29%22%22=%22%22f%281%2Fsqrt%28x-1%29%29%22%22=%22%221%22%22%2B%22%22matrix%282%2C1%2C%22%22%2C%281%5B%22%22%5D%29%2F%28%281%2Fsqrt%28%28x-1%29%29%29%5E2%29%29%22%22=%22%22

1%22%22%2B%22%22matrix%282%2C1%2C%22%22%2C%281%5B%22%22%5D%29%2F%28%281%2F%28x-1%29%29%29%29%22%22=%22%221%2B%28x-1%29%22%22=%22%221%2Bx-1%22%22=%22%22x

 Edwin