Answer:
The function can be written as y = u^3 + 2u^2 - 1 in terms of u.
Explanation:
The expression represents a polynomial function with two terms:
(x^((1)/(2)) + 3)^(3) and 2(x^((1)/(2)) + 3)^(2).
The term (x^((1)/(2)) + 3) represents a square root function added to a constant, and it is raised to the power of 3.
The term 2(x^((1)/(2)) + 3)^(2) represents the same square root function added to a constant, and it is raised to the power of 2.
The constant term -1 is subtracted from the sum of these two terms.
To rewrite the function y = (x^((1)/(2)) + 3)^(3) + 2(x^((1)/(2)) + 3)^(2) - 1 in composite form, we can introduce a new variable, let's say u, to represent the expression (x^((1)/(2)) + 3).
Then the function can be written as:
y = u^3 + 2u^2 - 1
Now, we can express the function in terms of u.
Thus,
The function can be written as y = u^3 + 2u^2 - 1 in terms of u.
Question:
Write the function in terms of u.
y = (x^((1)/(2))+3)^(3)+2(x^((1)/(2))+3)^(2)^{-1}