Question

Let f and g be the functions defined by f(x) = 10^ (x+2 / 3) and g(x) = log (x3 / 100) for all positive real numbers,

x. (Here the logarithm is a base-ten logarithm.)
Verify by composition that f and g are inverse functions to each other.

Answer 1

F(x) and g(x) are not inverse functions.

Explanation:

In order to calculate the inverse function of a function, we have to isolate X and after that, we change the variables.

As our function f(x) is a exponentian function, we can apply logarithm with base 10 (log) in both sides in order to isolate X. Remember that log10=1.

`[tex]y=10^{(x+(2)/(3)) }\\\\log y=log 10^{(x+(2)/(3)) }\\log y = (x+(2)/(3)) . log10\\(log Y)/(log10) = (x+(2)/(3))\\(log Y)/(1) = (x+(2)/(3))\\log Y-(2)/(3)=x`[/tex]

Now we change the variables.

`F(x)=log x-(2)/(3)`

F(x) and g(x) are not inverse functions.