Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=3x+5 \mathrm{and} g\left(x\right)=2x+1$

$$\begin{gathered} \left(a\right) Solve f\left(x\right)=g\left(x\right) \\ \left(b\right) Solve f\left(x\right)>g\left(x\right) \end{gathered}$$

Step-by-Step Solution

Answer

Part (a). The value of  $x=-4$.

Part (b). The value of $x>-4$.

Step 1. Given information.

The given function are $f\left(x\right)=3x+5 \mathrm{and} g\left(x\right)=2x+1$.

Part (a) Step 1. Solve for f ( x ) = g ( x ) .

$$\begin{gathered} f\left(x\right)=g\left(x\right) \\ 3x+5=2x+1 \\ 3x-2x=1-5 \\ x=-4 \end{gathered}$$

So, when $x=-4$ the value of $f\left(x\right) \mathrm{and} g\left(x\right)$ are the same.

Check: 

$$\begin{gathered} f(-4)=3·\left(-4\right)+5=-7 \\ g(-4)=2·(-4)+1=-7 \end{gathered}$$

Part (b) Step 1. Solve f ( x ) > g ( x ) .

$$\begin{gathered} f\left(x\right)>g\left(x\right) \\ 3x+5>2x+1 \\ 3x-2x>1-5 \\ x>-4 \end{gathered}$$

So, when the value of the $x>-4$ then the values of the $f\left(x\right)$ are greater than the values of $g\left(x\right)$.