2. The function $f(x)$ is an even function with the domain $\mathbf{R}$, and it is decreasing on $(0,+\infty)$. Which of the following inequalities holds? $($
A. $f\left(-\frac{3}{4}\right)>f\left(a^{2}-a+1\right)$.
B. $f\left(-\frac{3}{4}\right) \geqslant f\left(a^{2}-a+1\right)$.
C. $f\left(-\frac{3}{4}\right)<f\left(a^{2}-a+1\right)$.
D. $f\left(-\frac{3}{4}\right) \leqslant f\left(a^{2}-a+1\right)$.
2. From the definition of an even function, we know that $f(|x|)=f(x)$. Using this conclusion, we only need to compare $f\left(\left|-\frac{3}{4}\right|\right)$ with $f\left(a^{2}-a+1\right)$. And $a^{2}-a+1=\left(a-\frac{1}{2}\right)^{2}+\frac{3}{4} \geqslant \frac{3}{4}$.
Since $f(x)$ is a decreasing function on $(0,+\infty)$, we have $f\left(-\frac{3}{4}\right) \geqslant f\left(a^{2}-a+1\right)$, so the answer is B,