let f(x)= -5x/(2x^2+x-15). find the domain of f.

Question

How do I solve this?

Answer 1

f(x) = -5x /(2x² + x - 15)

Factorize the denominator

 

f(x) = -5x / 2x² +6x - 5x -15) = -5x/ 2x(x+3) - 5(x+3) =  -5x/(2x-5)(x+3)

 

2x-5 ≠ 0, x ≠ 5/2

and

x+3 ≠ 0, x≠ -3

 

Domain of f(x)

All values of x accept

x ≠ 5/2

x≠ -3

:)

Answer 2

Hi Cory;

We are going to focus on the denominator.  It cannot equal zero.

2x²+x-15

For the FOIL...

FIRST must be (2x)(x)=2x²

OUTER and INNER must add up to 1x, also known as x.

LAST must be (1)(15) or (15)(1) or (3)(5) or (5)(3) and one number must be zero to render the product of -15.

(2x-5)(x+3)

FIRST...(2x)(x)=2x²

OUTER...(2x)(3)=6x

INNER...(-5)(x)=-5x

LAST...(-5)(3)=-15

2x²+6x-5x-15

2x²+x-15

(2x-5)(x+3)

Either or both parenthetical equation(s) must equal zero...

2x-5=0....x+3=0

2x=5.......x=-3

x=5/2

Domain is...

(-infinity,-3)U(-3,5/2)U(5/2,+infinity)