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Question

Let f(x)=2xx2 and g(x)=cosx. Check given statement is true or not?
I. Domain of f(g(x)) = Domain of f(g(x)).

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Solution

f(x)=2xx2 and g(x)=cosx

y1=f(g(x))=2cosxcos2x

For existance of y1,2cosxcos2x0

cos2x+cosx20

(cosx1)0

D(y1)xR (cosx[1,1]xR)

y2=g(f(x))=cos(2xx2)

For existance of y2,2xx2R, we know that,

xR,2xx2R

D(y1)=D(y2)

This statement is true.

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