Question #N783
The function $f(x)$ is defined as $f(x) = \frac{1}{x^2+1}$. What is the value of $f(\frac{1}{2})$?
A. $\frac{1}{5}$
B. $\frac{2}{5}$
C. $\frac{4}{5}$
D. $\frac{5}{4}$
Correct Answer is: A
Substituting $\frac{1}{2}$ for $x$ in the equation $f(x) = \frac{1}{x^2+1}$ yields $f(\frac{1}{2}) = \frac{1}{(\frac{1}{2})^2+1}$. Simplifying the denominator gives us $f(\frac{1}{2}) = \frac{1}{\frac{1}{4}+1}$, or $f(\frac{1}{2}) = \frac{1}{\frac{5}{4}}$. Dividing 1 by $\frac{5}{4}$ is the same as multiplying by $\frac{4}{5}$, so $f(\frac{1}{2}) = \frac{4}{5}$.