Question

I need help solving this problem f(x)=2x^2+1 find and simplify f(x+2)-f(x)/2?

Answer 1

`f(x+2)-f(x)/2=x^2+8x+17/2`

Explanation:

`f(x) = 2x^2 + 1`

`f(x+2) - f(x)/2`

First, find `f(x+2)` by plugging `x+2` into the original equation

`f(x+2) = 2(x+2)^2 + 1`
`f(x+2) = 2(x^2+4x+4) + 1`
`f(x+2) = 2x^2+8x+9`

Next, find `f(x)/2` by substituting `2x^2+1` for `f(x)`

`f(x)/2 = (2x^2+1)/2`
`f(x)/2 = x^2+1/2`

Combine your answers for the final answer by substitution

`f(x+2) - f(x)/2`
`= (2x^2+8x+9) - (x^2+1/2)`
`=x^2+8x+17/2`

Answer 2

`x^2+8x+17/2`

Explanation:

`f(x+2)-f(x)/2`
`" "`
`=2(x+2)^2+1-(2x^2+1)/2`
`" "`
`=2(x^2+4x+4)+1-(2x^2)/2-1/2`
`" "`
`=2x^2+8x+8+1-x^2-1/2`
`" "`
`=2x^2-x^2+8x+8+1-1/2`
`" "`
`=x^2+8x+17/2`