Question

What is the range of `f(x)=x^2+2x-8`?

Answer 1

`[-9,oo)`.

Explanation:

`f(x)=x^2+2x-8=(x^2+2x+1)-9=(x+1)^2-9`.

`AA x in RR, (x+1)^2 ge 0`.

`:. (x+1)^2-9 ge -9......[because," adding "-9]`.

`rArr AAx in RR, f(x) ge-9`.

`:."The Range of "f" is " [-9,oo)`.