Question

Which statements represent the relationship between `y=3^x` and `y=log_3x` ?

Answer 1

1 and 3.

Explanation:

To test whether two functions are inverses of each other, we use the fact that if they are, then:

For two functions `f(x)` and `g(x)`:

`f(g(x))=x` and `g(f(x))=x`

This also means:

`f(g(x))=g(f(x))`

`3^(g(x))=log_3(f(x))`

`3^(log_3(x))=log_3(3^x)`

( This employs the laws of logarithms and exponents )

`x=x`

So the two functions are inverses of each other.

The function and its inverse are always symmetrical about the line:

`y=x`

This is not surprising, since the output of the function is the input of the inverse function and vice versa:

GRAPH: