Question

It has a fraction in it and will not let me type it out but says Given f(x)=8-2x², compute:

Answer 1

Given the function:

`f\mleft(x\mright)=8-2x^2`

1. You need to substitute this value of "x" into the function and evaluate:

`x=4`

In order to find:

`f(4)`

Then, you get:

`f(4)=8-2(4)^2=8-2(16)=8-32=-24`

2. Substitute this value of "x" into the function:

`x=2`

In order to find:

`f(2)`

Then, you get:

`f(2)=8-2\mleft(2\mright)^2=8-2(4)=8-8=0`

3. Substitute this value into the function and then evaluate:

`x=3`

In order to find:

`f(3)`

Therefore, you get:

`f(3)=8-2\mleft(3\mright)^2=8-2(9)=8-18=-10`

4. Given:

`(f(4)-f(2))/(4-2)`

Substitute the corresponding output values and simplify:

`=(-24-0)/(2)=(-24)/(2)=-12`

5. Given:

`(f(4)-f(3))/(4-3)`

Substitute the corresponding output values and simplify:

`=(-24-(-10))/(4-3)=(-24+10)/(1)=-14`

Hence, the answers are:

`\begin{gathered} (f(4)-f(2))/(4-2)=-12 \\ \\ \\ (f(4)-f(3))/(4-3)=-14 \end{gathered}`