Given f of x is equal to 2 divided by the quantity x squared plus 3x minus 10 end quantity, which of the following is true?
f(x) is positive for all x<-5
f(x) is negative for all x<-5
f(x) is positive for all x<2
f(x) is negative for all x>2

Respuesta :

Option B is the correct answer i.e. f(x) is negative for all x<-5

What is Function?

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, given function;

   f(x) = 2/(x²+3x-10)

   f(x) = 2/ (x²+5x-2x-10)

   f(x) = 2/ {x(x+5)-2(x+5)}

  f(x) = 2/ (x+5)(x-2)

Now, x+5 is positive from x>-5 and negative x < -5

        x-2 is positive from x > 2 and negative from x < 2

From above statement we can conclude that

         f(x) is negative for all x<-5

Thus, option B is the correct answer i.e. f(x) is negative for all x<-5.

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