Relations and Functions

If the domain of the function f(x)= x2-25 (4-x2 )+ 10 (x2+2x-15 ) is (- , ) [ , ), then 2+ 3 is equal to :

1. 140
2. 175
3. 125
4. 150

Answer

(4) 150

Solution

x2-25 0 x (- ,-5] [5, )

4-x2 0 x 2

x2+2x-15>0 (x+5)(x-3)>0 x (- ,-5) (3, )

Domain (common part) =(- ,-5) [5, )

at x=-5 the log argument is 0, so -5 is excluded

=-5, =5

2+ 3=25+125=150

Answer: (4)