Question

$\text{For the function}g\left(x\right)=5x^2-x-4,\text{find (a)}g(-2)\text{(b)}g(-1)\text{(c)}g\left(0\right)\text{.}$

Short answer

The value of f(x) for each part is

ⓐ 20

ⓑ 2

ⓒ −4

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Thegivenfunctionis}g\left(x\right)=5x^2-x-4,\\ \text{Wehavetofind(a)}g(-2)\text{(b)}g(-1)\text{(c)}g\left(0\right)\text{.}\end{array}$

Step 2. Substitute x=−2 in gx

$\begin{array}{l}\text{Wehave}g\left(x\right)=5x^2-x-4\\ \text{At}x=-2,\text{wehave}\\ \Rightarrow g(-2)=5{\left(-2\right)}^2-\left(-2\right)-4\\ =5\left(4\right)+4-4\\ =20+4-4\\ =20\end{array}$

Step 3. Substitute x=−1 in gx

$\begin{array}{l}\text{Wehave}g\left(x\right)=5x^2-x-4\\ \text{At}x=-1,\text{wehave}\\ \Rightarrow g(-1)=5{\left(-1\right)}^2-\left(-1\right)-4\\ =5\left(1\right)+1-4\\ =5+1-4\\ =2\end{array}$

Step 4. Substitute x=0 in gx

$\begin{array}{l}\text{Wehave}g\left(x\right)=5x^2-x-4\\ \text{At}x=0,\text{wehave}\\ \Rightarrow g\left(0\right)=5{\left(0\right)}^2-\left(0\right)-4\\ =5\left(0\right)+0-4\\ =0+0-4\\ =-4\end{array}$