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Question

If f(x)=ax+b, g(x)=cx+d, then fg(x)=gf(x) is equivalent to:


A

fa=gc

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B

fb=gb

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C

fd=gb

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D

fc=ga

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Solution

The correct option is C

fd=gb


Explanation for the correct option.

Find the relation:

fg(x)=acx+d+b=acx+ad+b...(1)

Similarly,

gf(x)=cax+b+d=acx+cb+d...(2)

It is given that fg(x)=gf(x), so

acx+ad+b=acx+cb+d⇒ad+b=cb+d⇒fd=gb

Hence, option C is correct.


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