Plz give step by step explanation on how to solve this not just answer.

y = (x + 2)² or y = x² + 4x + 4

Step-by-step explanation:

Consider the functions f(x) = x² and g(x) = x + 2

If y is defined as y = f(g(x)), state the equation for y.

Remember: The inside of the parentheses is done first.

So, we need to find g(x) first, which is x+2.

Now, substitute this into f(g(x)).

f (x + 2)

Now, because f(x) = x², we need to square (x+2)

f (x + 2) = (x + 2)²

(x + 2)(x +2) = x² + 2x + 2x + 4 = x² + 4x + 4

Thus, y = (x + 2)² or y = x² + 4x + 4

Just in case, let's check the answer.

Pretend that x = 3.

Then, g(x) = 5, and f(g(x)) = f(5) = 5² = 25.

Try this with the answer we got:

(x + 2)² = (3 + 2)² = 5² = 25

Or,

3² + 3*4 + 4 = 9 + 12 + 4 = 25

All three of these equations equal 25, so the answer is right.

So, the answer is correct.

I hope this helps! Feel free to ask any questions! :)