Chapter 8.6, Problem 73HP

To determine

To find: The value of expression which represents $f\left[g\left(x\right)\right]$ .

Answer to Problem 73HP

The value of the expression is $x^2-6x+8$ and the correct option is $\text{B}$ .

Explanation of Solution

Given information:

The given function is $f\left(x\right)=x^2+4x+3$ and $g\left(x\right)=x-5$ .

Calculation:

Consider the function.

  $f\left(x\right)=x^2+4x+3$

  $g\left(x\right)=x-5$

Thus,

  $\begin{array}{c}f\left[g\left(x\right)\right]={\left(x-5\right)}^2+4\left(x-5\right)+3\\ =x^2-10x+25+4x-20+3\\ =x^2-6x+8\end{array}$

Therefore, the value of the expression is $x^2-6x+8$ and the correct option is $\text{B}$ .