if f(x) = ex and g(x) = log x show that fog=gof given x>0

Question

relations and functions: composition of functions

Answer 1

Remeber the formulae e^lnx = x if x > 0 and ln(e^x) =x

Given functions are f(x) = e^x and g(x) = logx

fog = fog(x) = f(g(x))

= f(logx)

= e^logx

= x

gof = gof(x) = g(f(x))

= g(e^x)

= loge^x

= x

fog = gof