Chapter 2.1, Problem 4QR

To determine

Tofind: The value of $f\left(2\right)$ for $f\left(x\right)=\{\begin{array}{l}3x-1,x<2\\ \frac{1}{x^2-1},x\ge 2\end{array}$ .

Answer to Problem 4QR

The value of $f\left(2\right)$ for $f\left(x\right)=\{\begin{array}{l}3x-1,x<2\\ \frac{1}{x^2-1},x\ge 2\end{array}$ is $\frac{1}{3}$ .

Explanation of Solution

Given information:

The function is $f\left(x\right)=\{\begin{array}{l}3x-1,x<2\\ \frac{1}{x^2-1},x\ge 2\end{array}$ .

Calculation:

The function defined for the value $x=2$ is $f\left(x\right)=\frac{1}{x^2-1}$ .

Substitute $2$ for $x$ in the corresponding function.

  $\begin{array}{c}f\left(2\right)=\frac{1}{2^2-1}\\ f\left(2\right)=\frac{1}{4-1}\\ f\left(2\right)=\frac{1}{3}\end{array}$

Therefore, the value of $f\left(2\right)$ for $f\left(x\right)=\{\begin{array}{l}3x-1,x<2\\ \frac{1}{x^2-1},x\ge 2\end{array}$ is $\frac{1}{3}$ .