To express the function [tex]\( f(x) \)[/tex] more clearly, let's break it down step by step by simplifying each term:
1. Simplify each coefficient:
[tex]\[\frac{4}{3}\][/tex] remains [tex]\(\frac{4}{3}\)[/tex].
For the second term:
[tex]\[\frac{4}{5}\][/tex] remains [tex]\(\frac{4}{5}\)[/tex].
For the third term:
[tex]\[\frac{4}{4}\][/tex] simplifies to [tex]\(1\)[/tex].
2. Combine these coefficients with the corresponding powers of [tex]\( x \)[/tex]:
So, the function [tex]\( f(x) \)[/tex] can be rewritten as:
[tex]\[
f(x) = \frac{4}{3} x^3 - \frac{4}{5} x^2 + 1 \cdot x
\][/tex]
3. Express as a single polynomial:
Now, let's combine everything into a single polynomial expression. Here we simply keep the coefficients:
[tex]\[
f(x) = \frac{4}{3} x^3 - \frac{4}{5} x^2 + x
\][/tex]
But we are asked to express it in decimal form. The simplified numeric forms of the coefficients are:
- [tex]\(\frac{4}{3} \approx 1.33333333333333\)[/tex]
- [tex]\(\frac{4}{5} \approx 0.8\)[/tex]
- [tex]\(1 \approx 1.0\)[/tex]
So, the polynomial in decimal form is:
[tex]\[
f(x) = 1.33333333333333 x^3 - 0.8 x^2 + 1.0 x
\][/tex]
This is the detailed, step-by-step formation of the given polynomial function [tex]\( f(x) \)[/tex].
