Solve y = 3/4x²: Finding Positive Value Domains

To determine where the function $y = \frac{3}{4}x^2$ is positive, observe:

• **Step 1:** Identify the nature of the expression $x^2$.
  • The expression $x^2$ is always non-negative for any real number $x$, meaning $x^2 \geq 0$.
• **Step 2:** Consider when $x^2$ equals zero.
  • We see that $x^2 = 0$ only when $x = 0$, as any other value will yield a positive $x^2$.
• **Step 3:** Analyze the entire function.
  • The term $\frac{3}{4}$ is positive. Hence, $\frac{3}{4}x^2$ becomes positive whenever $x^2 > 0$, which implies $x \ne 0$.
  • Therefore, for all non-zero $x$, $y = \frac{3}{4}x^2 > 0$.

Thus, the function $y = \frac{3}{4}x^2$ is positive for all $x \ne 0$.

Therefore, the correct answer is $x \ne 0$.