Q48. - Algebra 2

Question

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

 

$g\left(\frac{1}{3}\right)$

Step-by-Step Solution

Answer

The value of $g\left(\frac{1}{3}\right)$ is $-\frac{2}{9}$.

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 $g\left(\frac{1}{3}\right)$} is $g\left(x\right)=x^2-x$.

Step 2 – Substitute the value in the selected function.

Substitute $x=\frac{1}{3}$ in the function $g\left(x\right)$.

$g\left(\frac{1}{3}\right)={\left(\frac{1}{3}\right)}^2-\left(\frac{1}{3}\right)$

Step 3 – Calculate the value by simplification.

$\begin{array}{l}g\left(\frac{1}{3}\right)={\left(\frac{1}{3}\right)}^2-\left(\frac{1}{3}\right)\\ g\left(\frac{1}{3}\right)=\frac{1}{9}-\frac{1\times 3}{3\times 3}\\ g\left(\frac{1}{3}\right)=\frac{1}{9}-\frac{3}{9}\\ g\left(\frac{1}{3}\right)=\frac{1-3}{9}\\ g\left(\frac{1}{3}\right)=-\frac{2}{9}\end{array}$

Thus, the value of $g\left(\frac{1}{3}\right)$ is $-\frac{2}{9}$.