Answer
$(-1,1)$
Work Step by Step
We are given the inequality:
$x^2-1<0$
$f(x)=x^2-1$
Determine the intercepts:
$y$-intercept: $f(0)=0^2-1=-1$
$x$-intercepts: $x^2-1=0$
$(x+1)(x-1)=0$
$x+1=0$ or $x-1=0$
$x=-1$ or $x=1$
The $y$-intercept is -1; the $x$-intercepts are -1 and 1.
Determine the vertex:
$x_V=-\dfrac{b}{2a}=-\dfrac{0}{2(1)}=0$
$y_V=f(x_V)=0^2-1=-1$
The vertex is $V(0,-1)$.
Graph the function.
The graph is below the $x$-axis for:
$x\in (-1,1)$
The solution set is:
$(-1,1)$
