Find the inverse function?

Question

of f(x)=10x .... and also log(base 10)x

Answer 1

For the first one: the inverse is g(x)=(1/10)x. Because (1/10)*(10x) = x.

For the second one: the inverse is g(x)=10^x. Because 10^(log x) = x.

Answer 2

The way to find inverse functions is to swap x and y (use y for f(x)) then solve for y.

For example, change the first one to

x = 10y

y = x/10 is the inverse function

For the second one, change to exponential form to solve for y

x = log y

y = 10^x is the inverse function.