Given that f (√ x + 1) = x + 2 √ x, try to determine the analytic formula F (x) Why can the number of substitution be directly converted to x?

Given that f (√ x + 1) = x + 2 √ x, try to determine the analytic formula F (x) Why can the number of substitution be directly converted to x?

These two XS are not the same
This x is different from the X in the function,
This is x = √ x + 1. Let's look at the simplification first
Let a = √ x + 1, x = (A-1) ^ 2
So f (a) = the absolute value of (A-1) ^ 2 + 2 (A-1)
In fact, the function is this, where a = √ x + 1
Attention! Attention
In order to facilitate the students' habits, we change a into x directly
Got it!