Answer
True for all $x$
$(-∞,+∞)$
Work Step by Step
Let $4x^2 - 4x + 1 \geq 0$ be a function $f$.
Find the $x$-intercepts by solving $4x^2 - 4x + 1=0$
Factor: $4x^2 - 4x + 1$ = $(2x-1)^{2}$
$2x-1=0$
$x = \frac{1}{2}$
In this case, there is exactly one $x$-intercept. The graph of the quadratic equation does not cross the $x$-axis but will only touch it at point $(\frac{1}{2},0)$.
Since we are interested in solving $f (x) \geq 0$, the inequality is true for all values of $x$ because the graph is always above the $x$-axis.
