Math II QUESTION from SparknOteS!!

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1

<p>So here's the problem:</p>

<p>f(x) = 2x^2 + 4 for –3 < x < 5. What is the range of f?
The best way to solve this type of problem is to manipulate the domain of x in exactly the same way that x is manipulated in the function. First x is squared, then multiplied by 2, then added to 4; we need to do the same thing to the bounds of the domain:
–3 < x < 5
0 < x^2 < 25
0 < 2x^2 < 50
4 < 2x^2 + 4 < 54
The range of f(x) is {4 < f(x) < 54}.</p>

<p>I don't understand the second step. Isn't (-3)^2= 9 not 0???
I am supremely confused.
Help!</p>

2

<p>Because x is squared, it cannot be negative. If you look at the graph of x^2, you'll notice the lower limit is not (-3)^2=9, but rather 0, which takes place at x=0.</p>

3

<p>Omg. I writing a paragraph on how I didn't get your explanation and then midway I got it!!
<em>dances around</em>
!!
Thank youuuu</p>

4

<p>how could it be possible ? </p>

<p>try x=0 than f(x)=4 </p>

<p>and naturally f(x) must be also EQUAL to 4 ???</p>

<p>am i wrong ?</p>