Please help me solve this problem

[bagofchips123]

Hi, I'm struggling to solve part b of this question. I understand I'm trying to find all values x for which f(x)=g(x), and need to look at each domain separately. In case 1 I discovered their is no intersection point, is that correct? Secondly, for case 2 I feel I'm required to use the quadratic formula however can't quite work out what the answer is, thus wether or not there is an intersection point. Thanks heaps

 

[Steven G]

You showed your work with the quadratic formula--thank you.
So what is the problem? Where are you stuck? Do you not know how to read the answer from the quadratic formula?

 

[bagofchips123]

You showed your work with the quadratic formula--thank you.
So what is the problem? Where are you stuck? Do you not know how to read the answer from the quadratic formula?

firstly it was of my understanding you can't have a negative square root, so should I cancel out the square root? Then from there how do I find the final answer. Also am I generally on the right track ? thank you

 

[Steven G]

Yes, you are on the right track.
You ask, should you cancel out the square root. What does that mean? Cancel out to what??

 

[HallsofIvy]

The square root of a number is always positive. That is why, generally, we have to write \(\displaystyle \pm\sqrt{x}\) in solutions of quadratic equation (such as the quadratic formula).

\(\displaystyle \sqrt{4}\) is 2 but \(\displaystyle \pm \sqrt{4}\) means both 2 and -2.