# Inequality question and don't know how this graph looks like?

Printable View

• Sep 14th 2010, 06:46 AM
dkssudgktpdy
Inequality question and don't know how this graph looks like?
1) What is the x values for:
x ( x - 5 ) > 0
--> my answers are x>0 and x>5. And the book says, x<0 and x>5

2) How does the graph of (4-x^2)^1/2 look like?

Thanks in advance!
• Sep 14th 2010, 07:01 AM
mathaddict
Quote:

Originally Posted by dkssudgktpdy
1) What is the x values for:
x ( x - 5 ) > 0
--> my answers are x>0 and x>5. And the book says, x<0 and x>5

2) How does the graph of (4-x^2)^1/2 look like?

Thanks in advance!

For (1), there are 2 cases to consider.

when x>0 and x-5>0, this implies x>0 and x>5

When x<0 and x-5<0 , this implies x<0 and x<5

Take the intersection of the solutions.

(2) Draw the graph $\displaystyle y_1= 4-x^2$ first.

We see that this graph intersects the x-axis at -2 and 2, the y-axis at 4

Now, for $\displaystyle y_2=\sqrt{4-x^2}$, for $\displaystyle -2\leq x\leq 2$ (Why? Think about the domain of a radical function)

Previously, y_1 intersects the y-axis at 4, now y_2 intersects at 2.

Put all these details together.
• Sep 14th 2010, 07:30 AM
dkssudgktpdy
so... for (1).. is the book answer wrong?
• Sep 14th 2010, 07:48 AM
Plato
Quote:

Originally Posted by dkssudgktpdy
so... for (1).. is the book answer wrong?

No the book's answer is correct.
Try some values: $\displaystyle x=3,~x=6,~x=-2$
Which work and which do not work?
Look at your answer.