Functions ..... pls do help.... questions are in the description

Question

1)-Let f(x)=|x^2-9|-|x-a|. Then the number of integers in the range of a do that f(x)=0 has 4 distinct real root is k . Then find the sum of the digit of K.

Ans-8

2)-Find the sum of all integral values of a where a belongs to [-10,10] such that the graph of the function f(x)=||x-2|-a|-3 has exactly three x-intercepts.

Ans-3

 

Answer 1

open any graphic calculator and plot the function from the first problem |x^2-9|-|x-a| . Of course, you need a number for a, since a is a parameter. play with the numbers a bit, put different ones instead of a.

 

From what I see you have 3 roots for |x^2-9|-|x+3|, four roots for -3<a<10, three roots for |x^2-9|-|x-10|.

 

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. So we have -2,-1,0,1,2,3,4,5,6,7,8,9

 

Could you count the sum of the digits now?

 

We could approach this problem in the more formal mathematical way also.