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Question

If f(x)=3x+24x1 and g(x)=x+24x3, prove that (gof)(x)=(fog)(x)=x.

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Solution

f(x)=3x+24x3 & g(x)=x+24x3
gof(x)=g(f(x))=g3x+24x1+243x+24x13=3x+2+8x212x+812x+3=11x11=x.
f(x)=x+24x3 & g(x)=x+24x3
gof(x)=g(f(x))=g3x+24x1+24x+24x11=3x+6+8x64x+84x+3=11x11=x.
fog(x)=gof(x)=x.

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