119k views
3 votes
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.

1 Answer

6 votes

Answer:

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.

User Vikramsjn
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.