Chapter 7: Q. 10 (page 450)

True or False $T h e d o m a i n o f y = \sin^{- 1} x i s - \frac{π}{2} \leq x \leq \frac{π}{2} .$

Short Answer

Expert verified

False Statement $T h e d o m a i n o f y = \sin^{- 1} x i s - \frac{π}{2} \leq x \leq \frac{π}{2} .$

Step by step solution

Step 1. Given Information:

Given statement:

$T h e d o m a i n o f y = \sin^{- 1} x i s - \frac{π}{2} \leq x \leq \frac{π}{2} .$

We want to know is the given statement is True or False.

Step 2. Solution:

If we know the range of the function then we can determine the domain of its inverse as follows:

Domain of the inverse function = The range of the original function.

We know that the range of the sine function is [- 1 , 1].

Therefore, the domain of the its inverse defined as y = sin^-1 x is equal to the range of the sine function which is [- 1 ,1].

Hence, the domain of y = sin^-1 x is $- 1 \leq x \leq 1$ so the statement is false.

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True or False $T h e d o m a i n o f y = \sin^{- 1} x i s - \frac{π}{2} \leq x \leq \frac{π}{2} .$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Solution:

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True or FalseThedomainofy=sin-1xis-π2≤x≤π2.

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Step 2. Solution:

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True or False $T h e d o m a i n o f y = \sin^{- 1} x i s - \frac{π}{2} \leq x \leq \frac{π}{2} .$