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

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1 Answer
Dec 19, 2017

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:

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