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How is the domain of a trigonometric function restricted so that its inverse function is defined?


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The graph of f(x)=tan(x) __________.

a. is one-to-one

b. does not pass the horizontal line test

c. does not pass the vertical line test


Therefore, a domain restriction must be placed on the function for the inverse function to be defined. The domain restriction placed on f(x)=tan(x) is _________ so that its inverse function is defined.

a. (-pi/2, pi/2)

b. (0, pi/2)

c. (0, pi)

d. [-pi/2, pi/2]

e. [0, pi/2]

f. [0, pi]

Respuesta :

Answer:

1. a. is not one-to-one

2. (-pi/2, pi/2)

Step-by-step explanation:

I just took the test, trust!

*make sure you use '(' brackets not '['.

f(x) = tan(x) is a trigonometric that is periodic, and the period can be

used to define the domain that defines the inverse function.

Response:

a. is one–to–one

[tex]\underline{a. \hspace{0.15 cm} \left( -\dfrac{\pi}{2}, \, \dfrac{\pi}{2} \right)}[/tex]

What properties of a function guaranty that the inverse is defined?

For the inverse of a function to be defined, the graph must pass the

horizontal line test for the inverse function to be defined.

Therefore;

The domain must be restricted such that f(x) = tan(x) has a one to one

relationship, that is within the domain, a value of f(x) has only one value

of x, from which the value of x can be determined from f(x), which makes

the inverse function also a function.

Therefore;

  • The graph of f(x) = tan(x) a. is one–to–one

For the given function, f(x) = tan(x), we have vertical asymptotes at [tex]-\dfrac{\pi}{2}[/tex], and [tex]\dfrac{\pi}{2}[/tex]

  • The restriction of the domain of f(x) = tan(x) is therefore;  [tex]\underline{a. \hspace{0.15 cm} \left( -\dfrac{\pi}{2}, \, \dfrac{\pi}{2} \right)}[/tex]

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