Sure, let's solve the given function step-by-step!
The function we are dealing with is:
[tex]\[ f(x) = 2x^8 - x^5 \][/tex]
Let's break this down:
1. Identify the components of the function:
- The first term is [tex]\( 2x^8 \)[/tex], which means 2 times [tex]\( x \)[/tex] raised to the power of 8.
- The second term is [tex]\(-x^5\)[/tex], which means [tex]\( -1 \)[/tex] times [tex]\( x \)[/tex] raised to the power of 5.
2. Combine the terms to form the function:
- Simply write the function combining the terms we identified:
[tex]\[ f(x) = 2x^8 - x^5 \][/tex]
3. Interpret the function:
- The function [tex]\( f(x) \)[/tex] is a polynomial with two terms.
- The highest power of [tex]\( x \)[/tex] is 8, so the degree of the polynomial is 8.
- The leading coefficient (coefficient of the term with the highest power) is 2.
- The term [tex]\(- x^5\)[/tex] affects the function by subtracting the value of [tex]\( x^5 \)[/tex].
This function can be plotted, analyzed for roots, or differentiated and integrated based on further requirements. But as it stands, this is the function we have:
[tex]\[ f(x) = 2x^8 - x^5 \][/tex]
