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

1. 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?

2. 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?

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 $y_1= 4-x^2$ first.

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

Now, for $y_2=\sqrt{4-x^2}$, for $-2\leq x\leq 2$ (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.

3. so... for (1).. is the book answer wrong?

4. Originally Posted by dkssudgktpdy
so... for (1).. is the book answer wrong?
No the book's answer is correct.
Try some values: $x=3,~x=6,~x=-2$
Which work and which do not work?