Evaluation of Functions Involving Radicals

In the 3rd Edition of Robert J Mergener's "Functions: An Approach to Algebra and Trigonometry," there is Problem #17 from Problem Set 1 - I have enclosed the file. The Answers to Odd Numbered Problems section says the answer should be 9-8*Radical 3 over 3. How do you get the answer?

 

To start, after the substitution of sqrt(3) for x, do you get:

3sqrt(3)^2 - 5sqrt(3) + 7/sqrt(3)

Assuming so, your next step is to do what is called rationalizing the denominator to the third term by multiplying top and bottom by sqrt(3).

Let us know what you have after that and if you can see the next step.

 

You'd think someone with a question would reply to someone trying to help them within 2 weeks.

 

The vast majority of questions, and profiles on this site are fake. Bot generated. You are kind to those you help. Thank you.

 

They don't care. It's that simple.

 

I do care Oculus. I don't understand what the disconnect here is. What sort of reply is needed from me? Furthermore, what sort of forum is this that people get scolded for not replying instantly? I appreciate Alonzo's help. Hopefully, you understand that.

 

Oops. My Bad Eddie.

I thought your post was from September 1, but I see now that it was from Saturday. September 1 was your join date. Apologies.

Having gotten that out of the way, your response would be to complete the calculation so we see you get the correct answer, or to show where you don't see the next step. Either one.

 

We have: 3x^2 - 5x + 7/x.

Replace every x in the function with sqrt{3} and do the math.

Here is the set up:

3(sqrt{3})^2 - 5(sqrt{3}) + 7/(sqrt{3})

Can you finish?

 

The process is called evaluation.

I have two more for you to practice.

1. Given -9x^2 - x + 1, evaluate when x = sqrt{5}.

2. Given 2x^3 + 4x - 7, evaluate when x = sqrt{7}.

 

Oculus - looks like you just repeated my next step suggestion.

 

I didn't copy you. Sometimes it is important to reinforce a certain skill to give students the confidence they often lack.