If ƒ(x) = 2x² + 3, then which of the following represent ƒ(x + 1)?
2x² + 2
x² + 3
2x² + 4x + 1
2x² + 4x + 5 

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A, at least to a single element 'b' of another non-empty set B. 

A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. 

f = {(a,b)| for all a ∈ A, b ∈ B}

It is given that

ƒ(x) = 2x² + 3

For f(x + 1) we have to substitute x as x + 1

f(x + 1) = 2(x + 1)² + 3

Using the algebraic identity (a + b)² = a² + b² + 2ab

f(x + 1) = 2(x² + 1 + 2x) + 3

From the multiplicative distributive property

f(x + 1) = 2x² + 2 + 4x + 3

f(x + 1) = 2x² + 4x + 5

Therefore, 2x² + 4x + 5 represents f(x + 1).

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

Summary:

If ƒ(x) = 2x² + 3, then 2x² + 4x + 5 represents f(x + 1).