Question

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

A. 2x^2 + 2
B. x^2 + 3
C. 2x^2 + 4x + 1
D. 2x^2 + 4x + 5

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

option (d) is correct.

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

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.