Question

For the function $g\left(x\right)=4x-7$, evaluate the function.

1. $g\left(m^2\right)$
   
2. $g\left(x-3\right)$
   
3. localid="1644747294810" $g\left(x\right)-g\left(3\right)$

Short answer

Part (a) $g\left(m^2\right)=4m^2-7$

Part (b) $g\left(x-3\right)=4x-19$

Part (c) $g\left(x\right)-g\left(3\right)=4x-12$

Step-by-step solution

Part (a) Step 1.

Substitute $x=m^2$in localid="1644747562374" $g\left(x\right)=4x-7$,

localid="1644747601123" $\begin{array}{rcl}g\left(m^2\right)& =& 4\left(m^2\right)-7\\ & =& 4m^2-7\end{array}$

Part (b) Step 1.

Substitute $x-3$for $x$in $g\left(x\right)=4x-7$,

$\begin{array}{rcl}g\left(x-3\right)& =& 4\left(x-3\right)-7\\ & =& 4x-12-7\\ & =& 4x-19\end{array}$

Part (c) Step 1.

$\begin{array}{rcl}g\left(x\right)-g\left(3\right)& =& \left(4x-7\right)-\left(4\left(3\right)-7\right)\\ & =& 4x-7-\left(12-7\right)\\ & =& 4x-7-5\\ & =& 4x-12\end{array}$