Finding a Specific x When We Know the Specific Output y

(by a graphical method)

 

In the previous lesson you found that when we can solve for x, we can write the formula for the inverse function, .

We also showed an example of a function when we could not solve for x using .

Suppose we need to find out what x value created the output .

We could guess it. In this case it might only take a few seconds to see that works.

However, we don't need to guess. If we can graph the original function, we can use the concept of the inverse function to find x.

Recall that

This might bother you, but really the letter in the parenthesis is just a "placeholder." It just helps us identify where to substitute a value within the rule for f or its inverse.

Using this concept graphically is very easy.

  1. Just find the y value on the y-axis.

  2. Track horizontally to the graph of your function.

  3. Then go vertically to the x-axis.

  4. Your input is the x value.

Look at the graph video to the left to see how we should do this. Just follow the arrows from y  = -2 to x = -1.

 

 

Using the graph to the right answer the following: (Click on the graph to see a larger version.)

  1. The x so that . Answer:
  2. The x so that (to the nearest tenth). Answer:
  3. The x so that (to the nearest tenth). Answer: