Question

The values of $x^2$ for x > -3 is set of

• A. All positive real numbers
• B. All negative real numbers
• C. All non-positive real numbers
• D. All non-negative real numbers

Answer 1

The correct option is D

All non-negative real numbers

x > -3

x ∈ (-3, $\infty$)

$\Rightarrow$ x ∈ (-3,0) U [0,$\infty$)

x ∈ (-3,0) $\Rightarrow$ $x^2$ ∈ (0,9)

x ∈ [0,$\infty$) $\Rightarrow$ $x^2$ ∈ [0,$\infty$)

So, $x^2$ ∈ (0,9) U [0,$\infty$) $\Rightarrow$ $x^2$ ∈ [0,$\infty$)

So, values of $x^2$ is set of all non-negative real numbers.