Solve the following problems.
1. If the length and width of a rectangular lot in functions are L(x) = x + 5 and W(x) = x + 1 respectively, What will be the area of rectangular lot in function?
2. If the area of a rectangle in terms of x represent by a function f(x) = 3x³ + 8x² + 4x-8 and the width is g(x) = x + 2, What is the length of a rectangle in function?
Answers & Comments
1. The area of rectangular lot in function is (x² + 6x + 5) unit area.
2. The length of a rectangle in function is 3x² + 2x - [tex]\frac{8}{x+2}[/tex]
Algebraic operations on a function consist of addition, subtraction, multiplication and division.
Basically algebraic operations on a function can be solved just like ordinary algebraic operations.
Mathematically, if (f) is a function with the origin (Df), and (g) is a function with the origin (Dg). Then the algebraic operation on the function can be expressed as below:
f + g is defined as (f + g)(x) = f(x) + g(x)
with origin Df + g = Df ∩ Dg
f - g is defined as (f - g)(x) = f(x) - g(x)
with origin Df-g = Df ∩ Dg
f × g is defined as (f × g)( x) = f(x) × g(x)
with the origin Df × g = Df ∩ Dg
f ÷ g is defined as (f/g)(x) = f(x) / g(x)
with the origin Df/g = Df ∩ Dg - {x | g(x) = 0}
Step-by-step explanation:
Given:
1. L(x) = x + 5 and W(x) = x + 1
2. f(x) = 3x³ + 8x² + 4x-8 and the width is g(x) = x + 2
Question:
1. What will be the area of rectangular lot in function?
2. What is the length of a rectangle in function?
Solutions:
1. The area of rectangular lot in function
The area = L(x) × W(x)
= (x + 5) × (x + 1)
= x² + 5x + x + 5
= x² + 6x + 5
So, the area of rectangular lot in function is (x² + 6x + 5) unit area.
2. The length of a rectangle in function
The length = f(x) ÷ g(x)
= (3x³ + 8x² + 4x - 8) ÷ (x + 2)
= 3x² + 2x - [tex]\frac{8}{x+2}[/tex]
So, the length of a rectangle in function is 3x² + 2x - [tex]\frac{8}{x+2}[/tex]
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