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1 year ago

A rectangle has vertices at (0, 0), (3, 0), and (0,6). What is the area of the rectangle?

Mathematics

1 answer:

Alexxandr [17]1 year ago

7 0

First, set the coordinate points on a graph, and joint them to form a graph

By looking at the graph we can see that:

width : 3

length: 6

Area of a rectangle : Length x width : 6 x 3 = 18

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Determine the domain and range of (g ○ f)(x) if f of x is equal to 4 over the quantity x squared minus 4 end quantity and g(x) =

lara [203]

The domain and range of a function are the possible x and y values of the function.

The domain and the range of the function is: (a) $\mathbf{D:\{x \in R|x \ne -2,2\}}$ and $\mathbf{R:\{(-\infty,1) \cup (2,\infty)\}}$

The functions are given as:

$\mathbf{f(x) = \frac{4}{x^2 - 4}}$

$\mathbf{g(x) = x + 2}$

(g o f)(x) is calculated as:

$\mathbf{(g\ o\ f)(x) = g(f(x))}$

So, we have:

$\mathbf{(g\ o\ f)(x) = \frac{4}{x^2 - 4} + 2}$

Take LCM

$\mathbf{(g\ o\ f)(x) = \frac{4 + 2x^2 - 8}{x^2 - 4} }$

$\mathbf{(g\ o\ f)(x) = \frac{2x^2 - 4}{x^2 - 4} }$

Represent the denominator as follows, to calculate the domain

$\mathbf{x^2 - 4 \ne 0 }$

Add 4 to both sides

$\mathbf{x^2 \ne 4 }$

Take square roots of bot sides

$\mathbf{x \ne \±2 }$

Hence, the domain of the function is:

$\mathbf{D:\{x \in R|x \ne -2,2\}}$

On the graph of $\mathbf{(g\ o\ f)(x) = \frac{2x^2 - 4}{x^2 - 4} }$ (see attachment), the function does not have a value from y = 1 to 2.

Hence, the range is:

$\mathbf{R:\{(-\infty,1) \cup (2,\infty)\}}$

Read more about domain and range at:

brainly.com/question/1632425

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2 years ago

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