Chapter 1, Problem 17SGA

To determine

To find: $f\left(m+1\right)$

Answer to Problem 17SGA

  $\text{|}{m}^2+5m+4|$

Explanation of Solution

Given information:

  $f\left(x\right)=\text{ |}{x}^2+3x|$

Calculation:

Put $x=m+1$ in $f\left(x\right)$ and evaluated as follows:

  $\begin{array}{c}f\left(x\right)=\text{|}{x}^2+3x|\\ f\left(m+1\right)=\text{|}{\left(m+1\right)}^2+3\left(m+1\right)|\\ =\text{|}{m}^2+2m+1+3m+3|\\ =\text{|}{m}^2+5m+4|\end{array}$

Thus, the value of $f\left(x\right)$ is $\text{|}{m}^2+5m+4|$ .