Answer:
option (d) is correct.
[tex]f(x+1) = 2x^2+4x+5[/tex]
Step-by-step explanation:
Given : [tex]f(x) = 2x^2 + 3[/tex]
We have to choose out of given option which represent f(x + 1)
Consider the given function [tex]f(x) = 2x^2 + 3[/tex]
Since we have to find f( x + 1 ) , replace x by x + 1 in the given function f(x) , we have,
[tex]f(x+1) = 2(x+1)^2+3[/tex]
Using algebraic identity, [tex](a+b)^2=a^2+b^2+2ab[/tex] , we have,
[tex]f(x+1) = 2(x^2+1+2x)+3[/tex]
Simplify the expression by multiplying 2 with each term in bracket, we have,
[tex]f(x+1) = 2x^2+2+4x+ 3[/tex]
Simplify , we have,
[tex]f(x+1) = 2x^2+4x+5[/tex]
Thus, option (d) is correct.
