(x)=2x-3 & f[g(x)]=1\4x-5. Find f(x)

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I assume g(x)=2x-3, f(g(x))=f(2x-3)=1/(4x-5).

Let y=g(x)=2x-3, then x=(y+3)/2 and 4x=2(y+3)=2y+6, f(y)=1/(2y+6-5)=1/(2y+1).

Therefore f(x)=1/(2x+1).

CHECK

f(g(x))=1/(2g(x)+1)=1/(4x-6+1)=1/(4x-5).
by Top Rated User (1.2m points)

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