Solve y = -x² + 1: Finding Values Where Function is Positive

Look at the following function:

$y=-x^2+1$

Determine for which values of $x$ the following is true:

$f\left(x\right) > 0$

To solve the problem of finding the values of $x$ for which $f(x) = -x^2 + 1 > 0$, we'll follow these steps:

• Step 1: Begin with the inequality $-x^2 + 1 > 0$.
• Step 2: Rearrange it to $1 > x^2$.
• Step 3: Recognize this can also be expressed as $x^2 < 1$.
• Step 4: Since $x^2 < 1$, the solutions for $x$ are those values between $-1$ and $1$: $-1 < x < 1$.

Therefore, the values of $x$ for which $f(x) > 0$ are $-1 < x < 1$.