Function composition is a mathematical concept that involves combining two or more functions to create a new function. A real-life example of function composition might involve a company that uses a software program to calculate payroll. The program might use one function to calculate an employee's hourly rate based on their salary, and another function to calculate their total hours worked based on their timecard data. These two functions could be combined using function composition to create a new function that calculates the employee's total pay.
As for multiplying a binomial with a trinomial, here's an example:
(2x + 3)(4x² + 5x - 6)
To solve this, we use the distributive property of multiplication, which involves multiplying each term in one set of parentheses by each term in the other set of parentheses. We can break this down into three separate multiplications:
2x (4x² + 5x - 6) = 8x³ + 10x² - 12x
3 (4x^2 + 5x - 6) = 12x² + 15x - 18
Adding these two results together, we get:
(2x + 3)(4x² + 5x - 6) = 8x³ + 22x² + 3x - 18
Therefore, the product of the binomial (2x + 3) and the trinomial (4x² + 5x - 6) is 8x³ + 22x² + 3x - 18.
