If f (x) = ex and g(x) = logx ( x>0), find fog and gof. Is fog = gof? Share with your friends Share 2 Neha Sethi answered this 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:R→RAlso, gof(x)=gfx=gex=logeex=xlogee=xWe observe that Domain(gof)≠Domainfog∴fog≠gof Regards 10 View Full Answer Priya answered this Fog=eto the power logx 2 Anuj Sharma answered this fog=loge* gof=e raise to the power logx hence fog is not equal to gof 1
