Expert: Michael Tadesse - 9/19/2009

Question
QUESTION: There are a couple of questions from my math homework that I don't understand.
Could you please explain them to me?

3) Consider the √ key on your calculator.  Recall that √ means the positive squre root.
Then it asks the output if the input is 25, which is five, and then it says
e) State the domain of this function.
The back of my book with the answers says D={x1x≥0, xЄR} but I don't understand that or how to get that answer.  I know that xЄR means that x is a set of real numbers, but I don't know how to get the first part, x1x≥0.

5)Evaluate for y+f(x).
a)f(3)
b)f(5)
c)f(5-3)
d)f(5)-f(3)
The book says the answers are a)4, b)2, c)5 and d)-2.  I don't understand how to do these equations.

6)For g(x)=3-2x, find
e)g(-2)-3
The books says the answer is 4, but I don't understand how to get this.

11)Evaluate for g(x)=2x+3.
c)g(5)-g(3)
d)2g(3)-5
It says the answers are c)4 and d_13, and I don't understand how to get this.

Sorry there are a lot of questions, but I just really don't understand my teacher's way of teaching this.
Thanks a ton for any help!

ANSWER: Hello again, Kaitlyn

You see, the function represented by √, is as you said the square root function. And its properties are:

•   The inputs are always non-negative (0 or greater than 0)
•   The outputs are always non-negative

This means you can’t have any negative number as an output from the square root function. So you can define the domain and range. How? We will see.

The Domain of a function is the region of some elements (numbers) which the function can take for its independent variable. It is a set of eligible numbers which the function can operate with.

For instance, 1/x, you can see that all real numbers but 0 are eligible. You can’t divide any number by 0. So the domain of the function, 1/x is all real numbers with out 0.

Similarly, the domain of the square root function is the set of all non-negative numbers or
{X: X ≥ 0} which means the entire real line except those negative numbers are eligible to be operated by the square root function.


As for number 5, you didn’t give me the equation. May be next time try to

Problem #6

g(-2) means the value of the function with -2 substituted in X.

g(x) = 3 – 2x
g(-2) = 3 – 2(-2)
 g(-2) = 3 + 4
 g(-2) = 7

 So the next thing you’ve to do is subtract 3 from g (-2).

 7 – 3 = 4.




Problem #11

I hope you wouldn’t miss this one after you see the solution of problem 11. Try it yourself and check.

First find g(5) and g(3)

g(5) = 13 and g(3) = 9

So subtract them and you’ll get 4.
The same thing applies for the second one. Double the value of g(3) and subtract 5

The answer is given and it is 13 (18 – 5 = 13)







---------- FOLLOW-UP ----------

QUESTION: For number 3 I still don't understand what D={x1x≥0, xЄR} means, with all the symbols and everything.

I am sorry about number five.  I meant to type in the equation y=f(x) instead of y+f(x).  So y=f(x0 is the equation.  Can you please help me with that question now?

Number 6 makes sense now, thanks a bunch!

For number 11 I was able to solve c), but I can not figure out how to get d).  Can you please explain.

Thanks so much for all of your help, this stuff is starting to make sense to me.

Answer
Good to hear from you again Kaitlyn

Problem #3

D= {x1x≥0, xЄR} This is a typo, the number between the Xs is redundant. The author wanted to put the sign of such that. But the remaining is the same as I explained before.

Problem #5

I still have doubt with this problem. Pardon me. I don’t know the equation of y=f(x).

Problem #11

g(x) =2x+3.

2g (3)-5

Kaitlyn, look:

To find the value of 2g (3)-5, first find the value of g(3) and multiply it by 2
Then subtract 5 from it.

G(3) = 2(3) + 3
G(3) = 9

Now multiply it by two

9*2 = 18

Subtract 5 from it.

18 – 5 = 13