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