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

2 Answers
Feb 2, 2017

#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#

Feb 2, 2017

#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#