A Level maths exam question!

https://www.quora.com/profile/Bravewarrior/p-164632367
Here is the question with its solution. I am stuck on part b. I understand all the working but when I solved (x-2)^2 +1 = 28 I got two answers which were 2-3root3 and 2+3root3. I also solved 4x-7=28 which gave 35/4=x. Now the final solution says the x values are between 2-3root3 and 35/4. Why did they ignore the 2+3root3?

Reply 1

tonyiptony

Well, 2+3root(3) > 2, so it wouldn't be a valid solution for the "left half" of the piecewise function.

Reply 2

pigeonwarrior

Original post by tonyiptony

Well, 2+3root(3) > 2, so it wouldn't be a valid solution for the "left half" of the piecewise function.

I see it now, thank you! 🙂

Reply 3

math-path

Yes, you need to keep the x variable restrictions in mind when solving the separate equations.
Here is what you have:

Reply 4

pigeonwarrior

Original post by math-path

Yes, you need to keep the x variable restrictions in mind when solving the separate equations.
Here is what you have:

Thank you! It makes much more sense now 🙂

Reply 5

username5443984

Original post by pigeonwarrior

The domain restriction for g(x) is such that for x≤2, we use the function (x-2)^2 -1 so since 2 + 3√3 is > 2, we don't take this as a solution. Hope this was helpful.

Reply 6

pigeonwarrior

Original post by vnayak

The domain restriction for g(x) is such that for x≤2, we use the function (x-2)^2 -1 so since 2 + 3√3 is > 2, we don't take this as a solution. Hope this was helpful.