Question

Use the graph to find the appropriate solutions to the equation

Answer 1

The first thing that you should notice is that you have two functions:

`f(x)=\text{ -}2|x\text{ -}3|+1;\text{ and }g(x)=\text{ -}2\sqrt{x\text{ -}1}`

Then their respective graphs are given by the blue and the red functions in your picture. Now, the main idea, is to know the points where they are equal and in that way, you will have the initial equation as follows:

`f(x)=\text{ -}2|x\text{ - }3|+1=\text{ -}2\sqrt{x\text{ - }1}\text{ }=g(x)`

The equation will be satisfied in terms of their graphs at the points where they intersect themselves, at the x-coordinate.

The intersection points A and B at the x-coordinate are the answer for the equation. Then

`x\approx1.7\text{ or }x\approx5.7`