Question

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

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

Short answer

Part (a). The value of $x=-4$.

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

Step-by-step solution

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$g\left(x\right)$.