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

Answer:

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

Step-by-step 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.

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

Now we change the variables.

$F(x)=log x-\frac{2}{3}$

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