Return to Assignments Exponential functions and graphs

### Assignment 10

For which value(s) of do the graphs of the functions:

have only one point in common.

### Solution

In order to calculate the intersection points of and we have to solve the following equation:

Substituting:

in the equation we get:

This quadratic equation has two coinciding solutions if the discriminant , so if:

or

If we get , i.e. and this does not give a solution. Thus the value of for which both graphs have just one common point is .

Verify that the common point is , see the figure.