Question

In the following exercises, evaluate the function:

$$\begin{gathered} a.g\left(h^2\right) \\ b.g(x+2) \\ c.g\left(x\right)+g\left(2\right) \end{gathered}$$

Function:$g\left(x\right)=7-5x$

Short answer

The values of the function are:

$$\begin{gathered} a.g\left(h^2\right)=7-5h^2 \\ b.g(x+2)=-5x-3 \\ c.g\left(x\right)+g\left(2\right)=-4-5x \end{gathered}$$

Step-by-step solution

Step 1. Given Information

The given function is $g\left(x\right)=7-5x$.

Part (a) Step 1.  Evaluating g(h2)

To evaluate $g\left(h^2\right)$, substitute$h^2$for$x.$

$$\begin{gathered} g\left(h^2\right)=7-5\left(h^2\right) \\ g\left(h^2\right)=7-5h^2 \end{gathered}$$

Therefore,$g\left(h^2\right)=7-5h^2$.

Part (b) Step 1.  Evaluating g(x+2)

To evaluate $g(x+2),$substitute $x+2$for $x.$

$$\begin{gathered} g(x+2)=7-5(x+2) \\ g(x+2)=7-5x-10 \\ g(x+2)=-3-5x \end{gathered}$$

Therefore,$g(x+2)=-3-5x$

Part (c) Step 1.  Evaluating g(x)+g(2).

To evaluate $g\left(x\right)+g\left(2\right),$first evaluate $g\left(2\right)$.

$$\begin{gathered} g\left(2\right)=7-5\left(2\right) \\ g\left(2\right)=7-10 \\ g\left(2\right)=-3 \end{gathered}$$

Now find, $g\left(x\right)+g\left(2\right)$.

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

Therefore,$g\left(x\right)+g\left(2\right)=-5x-4$