Q44. - Algebra 1

Question

Examples 4 and 5 If $f\left(x\right)=-2x-3$ and $g\left(x\right)=x^2+5x,$ find each value. (P. 50)

$3\left[g\right(n\left)\right]$

Step-by-Step Solution

Answer

The value of the function is $3n\left(n+5\right)$

Step 1. Interpreting of function.

$g\left(n\right)$ Indicates the value of function $g\left(x\right)$ at $x=n$

Step 2. Apply substitution method.

Substitute $x=n$ into the function $g\left(x\right)$

$\begin{array}{l}g\left(n\right)={\left(n\right)}^2+5n\\ g\left(n\right)=n^2+5n\end{array}$

Step 3. Further calculation.

$\begin{array}{l}3\left[g\left(n\right)\right]=3\left[n^2+5n\right]\\ 3\left[g\left(n\right)\right]=3n^2+15n\\ 3\left[g\left(n\right)\right]=3n\left(n+5\right)\end{array}$

Thus, the value of the function is $3n\left(n+5\right)$