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! :)
