This is what I have forQuote:

For each of the following, 1- Determine the definite equation for f[g(x)] and g[f(x)]. 2- Determine the domain and range of f[g(x)] and g[f(x)]

e) f(x) = 10^x , g(x)= log x (log x base 10)

f[g(x)] = 10 ^ ( log x) = x

g[f(x)] = log 10^x = x.

f[g(x)] = {x E R , x > 0 } because in g(x) x can not be negative.......................... g[f(x)] = { x E R, x > 0 } because in g(x) x can not be negative

f[g(x)] ={y E R, y > 0}................................................ ....................................g[f(x)] = {y E R, y > 0}

However my text book says

f[g(x)] = {x E R , x > 0 } ......................g[f(x)] = { x E R }

f[g(x)] = { y E R} ...................... ... g[f(x)] ={y E R}

Who is right? Thank you in advance.