Q51. - Algebra 2

Question

Find each value if $f\left(x\right)=3x-5$ and $g\left(x\right)=x^2-x$.

$g\left(5n\right)$

Step-by-Step Solution

Answer

The value of $g\left(5n\right)$ is $25n^2-5n$.

Step 1 – Select the correct function.

_{The given functions are:}

_{$\begin{array}{l}f\left(x\right)=3x-5\\ g\left(x\right)=x^2-x\end{array}$}

_{The required function for the value $g\left(5n\right)$} is $g\left(x\right)=x^2-x$.

Step 2 – Substitute the value in the selected function.

Substitute $x=5n$ in the function $g\left(x\right)$.

$g\left(5n\right)={\left(5n\right)}^2-\left(5n\right)$

Step 3 – Calculate the value by simplification.

$\begin{array}{l}g\left(5n\right)={\left(5n\right)}^2-\left(5n\right)\\ g\left(5n\right)=5^2{n}^2-5n\\ g\left(5n\right)=25n^2-5n\end{array}$

Thus, the value of $g\left(5n\right)$ is $25n^2-5n$.