In a problem I was asked to find the domain of(adsbygoogle = window.adsbygoogle || []).push({});

f of f, which is f(f(x))

where f(x)=(ax+b)/(cx+d)

so I get: f((ax+b)/(cx+d))

(a)(ax+b)/(cx+d)

(c)(ax+b)/(cx+d)

after I multiply it out I get

(a^2x+ab+bcx+bd)/(cx+d)

(cax+bc+cdx+d^2)/(cx+d)

now the "cx+d" cancels and you are left with

(a^2x+ab+bcx+bd)/(cax+bc+cdx+d^2)

therefore x can't be equal to (cax+bc+cdx+d^2)

but when I try to reduce it into a form that works I get stuck with an x on both sides

x=(-bc-cd-cdx)/(ca)

Any help would be greatly appreciated. I have tried this problem several times and I continue to get the same answer but it dosent make sense to me. Also "x" obviously cant equal -d/c in the final answer

Thanks

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# Homework Help: Problem with composite functions

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