Question

Given f(x) = x² + 2x + 3, find f(x+5).

1) x² + 12x + 33
2) x² + 2x + 38
3) x² + 2x + 33
4) x² + 12x + 38

Answer 1

To find f(x+5) for the function f(x) = x² + 2x + 3, replace x with (x+5), expand and simplify the expression to find f(x+5) = x² + 12x + 38. option 4) is the correct answer.

Step-by-step explanation:

To find f(x+5), we need to substitute x+5 into the given function f(x) = x² + 2x + 3. Let's perform the substitution and simplify:

1. Replace every x in the function with (x+5).
2. Simplify the resulting expression.

So, we have:

f(x+5) = (x+5)² + 2(x+5) + 3

First, expand (x+5)² to get x² + 10x + 25. Then distribute the 2 to get 2x + 10. Adding all the terms together and simplifying:

f(x+5) = x² + 10x + 25 + 2x + 10 + 3

Combine like terms:

f(x+5) = x² + 12x + 38

Therefore, the correct choice is 4) x² + 12x + 38.