Question

I need to find f(x) and g(x)?? Anyone

Answer 1

f(g(x)) = x

g(f(x)) = x

are inverses

Explanation:

Given f(x) = x/(6+x) and g(x) = 6x/(1-x) you want f(g(x)) and g(f(x)).

F(g(x))

This composition of the two functions will be ...

`f(g(x))=f\left((6x)/(1-x)\right)=((6x)/(1-x))/(6+(6x)/(1-x))=((6x)/(1-x))/((6-6x+6x)/(1-x))=(6x)/(6)=x`

G(f(x))

This composition of the two functions will be ...

`g(f(x))=g\left((x)/(6+x)\right)=(6\cdot(x)/(6+x))/(1-(x)/(6+x))=((6x)/(6+x))/((6+x-x)/(6+x))=(6x)/(6)=x`

Summary

We have ...

• f(g(x)) = x
• g(f(x)) = x
• f(x) and g(x) are inverses of each other

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