Find functions f(x) and g(x) such that f(g(X)= sq root (x^2 + 1)

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Guest Jan 23, 2016

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Chris's answer is correct (and probably the one that was wanted) but it isn't unique!

For example we could also have f(x) = x and g(x) = (x^2 + 1)^(1/2)

or f(x) = x^2 and g(x) = (x^2 + 1)^(1/4)

or f(x) = x^3 and g(x) = (x^2 + 1)^(1/6)

or ... etc.

Alan Jan 23, 2016

Alan · Answer 1 · 2016-01-23T09:53:01

Chris's answer is correct (and probably the one that was wanted) but it isn't unique!

For example we could also have f(x) = x and g(x) = (x^2 + 1)^(1/2)

or f(x) = x^2 and g(x) = (x^2 + 1)^(1/4)

or f(x) = x^3 and g(x) = (x^2 + 1)^(1/6)

or ... etc.

CPhill · Answer 2 · 2016-01-23T08:44:54

Let f(x) = sqrt(x)

Let g(x) = x^2 + 1

So.....f(g(x)) means that we are putting g(x) into f (x) for x....and we have

sqrt(g(x)) = sqrt (x^2 + 1)