Hello there. To solve this question, we'll simply have to make x => x + 5 in the function.
Given the function:
We have to determine f(x + 5)
By making x => x + 5 in this function, we get:
Now remember the binomial expansion of order 2:
Therefore we have:
Multiply the terms inside parentheses and calculate the square.
Apply the distributive property
Multiply and add the numbers
This is the answer we're looking for.
A way of showing this is the correct answer is to make x = 1 and x = 6 in the former function:
Then making x = 1 in the expression we found after:
As expected.