To find the function [tex]\( y \)[/tex] in the question, let's start by carefully examining the expression given:
[tex]\[ y = \frac{(2x^2 + 1)^4}{2} \][/tex]
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### Step-by-step Solution:
1. Understanding the Expression:
- The given expression is a fraction where the numerator is [tex]\((2x^2 + 1)^4\)[/tex] and the denominator is 2.
2. Break Down the Term:
- The term [tex]\((2x^2 + 1)^4\)[/tex] indicates that inside the parentheses, [tex]\(2x^2 + 1\)[/tex] is raised to the fourth power.
3. Considering the Simplification Process:
- Understand that [tex]\((2x^2 + 1)^4\)[/tex] suggests distributing the exponent to everything inside the parentheses.
- However, because it is in a numerator over a denominator (2), there isn’t further simplification needed in fractional form.
4. Fraction Simplification Mechanics:
- The expression [tex]\(\frac{(2x^2 + 1)^4}{2}\)[/tex] intuitively indicates that the complex term [tex]\((2x^2 + 1)\)[/tex] is raised to the fourth power and then divided by 2.
To summarize, the function [tex]\( y \)[/tex] is:
[tex]\[ y = \frac{(2x^2 + 1)^4}{2} \][/tex]
This simplifies the expression and showcases that the given function involves a polynomial raised to a high power divided by a constant.
Remember this structure when working with polynomial functions of this nature and handling divisions involving exponents.
