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.