Question

Use the function to evaluate the indicated expression and simplify. f(x) = 2x^2 + 5; f(x+2), f(x) + f(2)

Answer 1

`f(x+2)=2x^2+8x+13`

`f(x) + f(2)= 2x^2+18`

Explanation:

Given function:

`f(x)=2x^2+5`

To find f(x + 2), substitute (x + 2) in place of x in the function:

`\begin{aligned}\implies f(x+2) & = 2(x+2)^2+5\\& = 2(x+2)(x+2)+5\\& = 2(x^2+4x+4)+5\\& = 2x^2+8x+8+5\\& = 2x^2+8x+13\end{aligned}`

To find f(x) + f(2), substitute x = 2 into the function and add this to the original function:

`\begin{aligned}\implies f(x) + f(2) & = [2x^2+5]+[2(2)^2+5]\\& = 2x^2+5+2(4)+5\\& = 2x^2+5+8+5\\& = 2x^2+18\end{aligned}`