Given the function:
[tex]f\mleft(x\mright)=8-2x^2[/tex]
1. You need to substitute this value of "x" into the function and evaluate:
[tex]x=4[/tex]
In order to find:
[tex]f(4)[/tex]
Then, you get:
[tex]f(4)=8-2(4)^2=8-2(16)=8-32=-24[/tex]
2. Substitute this value of "x" into the function:
[tex]x=2[/tex]
In order to find:
[tex]f(2)[/tex]
Then, you get:
[tex]f(2)=8-2\mleft(2\mright)^2=8-2(4)=8-8=0[/tex]
3. Substitute this value into the function and then evaluate:
[tex]x=3[/tex]
In order to find:
[tex]f(3)[/tex]
Therefore, you get:
[tex]f(3)=8-2\mleft(3\mright)^2=8-2(9)=8-18=-10[/tex]
4. Given:
[tex]\frac{f(4)-f(2)}{4-2}[/tex]
Substitute the corresponding output values and simplify:
[tex]=\frac{-24-0}{2}=\frac{-24}{2}=-12[/tex]
5. Given:
[tex]\frac{f(4)-f(3)}{4-3}[/tex]
Substitute the corresponding output values and simplify:
[tex]=\frac{-24-(-10)}{4-3}=\frac{-24+10}{1}=-14[/tex]
Hence, the answers are:
[tex]\begin{gathered} \frac{f(4)-f(2)}{4-2}=-12 \\ \\ \\ \frac{f(4)-f(3)}{4-3}=-14 \end{gathered}[/tex]
