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

Question

class 12 relations and functions

Answer 1

 f(x) = ex and g(x) = ln x

E is a special number  where e^x differentiates to e^x.  Ln (x) is Log base e of x.

Given that log base 10 of 10 is 1, and log base n of n is 1, ln(e) is also 1.  So fg(x) = e^(g(x)) = e^(log x) = x.  GF(x) = ln(f(x)) = ln(e^x)= x * ln(e) (using log laws, bringing power to the front), = x*1 = x.

 

Therefore fg(x) = x = gf(x)

Please let me know if this answer is any good or needs further explination.