Find-the-range-of-the-function-y-2-x-2-sin-x-x-0-

Question Number 101172 by I want to learn more last updated on 01/Jul/20

Find the range of the function :

y = 2 - x^{2} \sin (x), x ⩾ 0

Answered by 1549442205 last updated on 07/Jul/20

Since - 1 ⩽ sinx ⩽ 1, so : - x^{2} ⩽ x^{2} sinx ⩽ x^{2}

we infer : 2 - x^{2} ⩽ 2 - x^{2} sinx ⩽ 2 + x^{2}

\Rightarrow - \infty < y = 2 - x^{2} sinx < + \infty

The value domain of y : (- \infty; + \infty)

Commented by I want to learn more last updated on 01/Jul/20

Sir, is this the same thing as :

Range is all real numbers .

Commented by 1549442205 last updated on 01/Jul/20

the value domain of a function and

the range of a function are same concept