Chapter 6, Problem 13MCQ

To determine

Find the value of the expression using given functions.

Answer to Problem 13MCQ

The value of the given expression is $-a^2-9a+2$ .

Explanation of Solution

Given:

The given expression is $3f\left(a-4\right)-2h\left(a\right)$ and the given functions are $f\left(x\right)=x^2+3x$ and $h\left(x\right)=2x^2-3x+5$ .

Calculation:

The original function is

  $f\left(x\right)=x^2+3x$

Replace the $x$ in $f\left(x\right)$ with $a-4$ .

  $\begin{array}{l}f\left(a-4\right)={\left(a-4\right)}^2+3\left(a-4\right)\\ =a^2-8a+16+3a-12\\ =a^2-5a+4\end{array}$

The original function is

  $h\left(x\right)=2x^2-3x+5$

Replace the $x$ in $h\left(x\right)$ with $a$ .

  $h\left(a\right)=2a^2-3a+5$

Now,

  $\begin{array}{l}3f\left(a-4\right)-2h\left(a\right)\\ =3\left(a^2-5a+4\right)-2\left(2a^2-3a+5\right)\\ =3a^2-15a+12-4a^2+6a-10\\ =-a^2-9a+2\end{array}$

Hence the value of the given expression is $-a^2-9a+2$ .