If f (x) = ex and g(x) = logx ( x>0), find fog and gof. Is fog = gof?

Dear student
We have,Domainf=R,Rangef=0,,Domaing=0, and rangeg=RComputation of fog: We observe that Range(g)=0,Domain(f)=R fog exists and fog:Domain(g)R i.e., fog:0,RAlso,fog(x)=f(g(x))=f(logex)=elogex=xThus, fog:(0,)R is defined as fog(x)=xComputation of gof:WE have,Range(f)=0,=Domain(g)gof exists and gof:Domain(f)R i.e, gof:RRAlso, gof(x)=gfx=gex=logeex=xlogee=xWe observe that Domain(gof)Domainfogfoggof
Regards

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Fog=eto the power logx
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fog=loge*        gof=e raise to the power logx    hence fog is not equal to gof
 
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