Finding intersection between exponential and inverse function

[anonymous12]

Homework Statement

Given the exponential function and its inverse, where a > 0
Exponential Function:
$$f(x)=a^x$$
Inverse function:
$$f^{-1}(x)=log_ax$$

a) For what values of a do the graphs of f(x)=a^x and f^(-1)(x) intersect?

The Attempt at a Solution

I have no idea how to start this question.

Off topic: How do I make is so I can type a sentence and LaTeX on the same line?

 

[Mark44]

Homework Statement

Given the exponential function and its inverse, where a > 0
Exponential Function:
$$f(x)=a^x$$
Inverse function:
$$f^{-1}(x)=log_ax$$

a) For what values of a do the graphs of f(x)=a^x and f^(-1)(x) intersect?

The Attempt at a Solution

I have no idea how to start this question.

Off topic: How do I make is so I can type a sentence and LaTeX on the same line?

The graphs of y = f(x) and y = f^-1(x) are reflections of each other across the line y = x. Think about what the graphs of your two functions look like, especially in relation to the line y = x.

You can have text and LaTeX on the same line if you use [ itex ] and [ /itex ] tags (no spaces).