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Chapter 7: Q. 20 (page 503)

In Problems 9鈥�23, find the exact value, if any, of each composite function. If there is no value, say it is 鈥渘ot defined.鈥� Do not use a calculator.

tansin-1-32

Short Answer

Expert verified

The exact value of the composite function is-3.

Step by step solution

01

Step 1. Given Information 

The given composite function istansin-1-32.

We have to find the exact value.

02

Step 2. Finding the value 

To find the exact value, let x=sin-1-32.

Now, the domain of the sine function is -蟺2鈮�x鈮�蟺2.

The value of sin-1-32=-蟺3.

So, x=-蟺3because the value lies in the domain of the sine function.

03

Step 3. Solve the composite function 

Now, substitute thexvalue in the given function.

Thus,

tansin-1-32=tan-蟺3=-3

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