Q. 5.18 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

The value of f(x) for each part is  

ⓐ 20

ⓑ 2

ⓒ −4 

Step 1. Given information

$\begin{array}{l}\text{The given function is }g\left(x\right)=5x^2-x-4,\\ \text{We have to find (a) }g(-2)\text{ (b) }g(-1)\text{ (c) }g\left(0\right)\text{. }\end{array}$

Step 2. Substitute  x = − 2  in  g x

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

Step 3. Substitute  x = − 1  in  g x

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

Step 4. Substitute  x = 0  in  g x

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