Question

If ƒ(x) = 2x2 + 3, then which of the following represent ƒ(x + 1)?

Answer 1

Sub (x+1) for x

f(x+1)=2(x+1)^2+3
f(x+1)=2(x^2+2x+1)+3
f(x+1)=2x^2+4x+2+3
f(x+1)=2x^2+4x+5

D is answer

Answer 2

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.