The function f is defined by f x = 5 1 4 - x 2 +

The correct answer is $\frac{11}{4}$. It’s given that the function $f$ is defined by $f\left(x\right)=5{\left(\frac{1}{4}-x\right)}^2+\frac{11}{4}$. Substituting $\frac{1}{4}$ for $x$ in this equation yields $f\left(\frac{1}{4}\right)=5{\left(\frac{1}{4}-\frac{1}{4}\right)}^2+\frac{11}{4}$, which is equivalent $f\left(\frac{1}{4}\right)=5{\left(0\right)}^2+\frac{11}{4}$, or $f\left(\frac{1}{4}\right)=\frac{11}{4}$. Therefore, the value of $f\left(\frac{1}{4}\right)$ is $\frac{11}{4}$. Note that 11/4 or 2.75 are examples of ways to enter a correct answer.