Answer to Question #347336 in Calculus for Stella

Question

If f(x) =10^x and Φ(x) =log10 x, show that f[Φ(x)] = Φ [f(x)] = x.

Answer 1

$$f[\Phi(x)]=10^{\log_{10}x}=x, x>0$$

$$\Phi[f(x)]=\log_{10}{(10^x)}=x, x\in\R$$

Therefore

$$f[\Phi(x)]=\Phi[f(x)]=x, x>0$$