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