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Chapter 7: Q. 76 (page 458)

In Problems 67鈥�78, fx=sinx,-蟺2鈮�x鈮�蟺2,gx=cosx,0鈮�x鈮�蟺andhx=tanx,-蟺2<x<蟺2

Find the exact value of each composite function.

role="math" localid="1646624335863" g-1f-5蟺6

Short Answer

Expert verified

The required exact value of given expression is 2蟺3.

Step by step solution

01

Step 1. Given information. 

The composite functiong-1f-5蟺6.

02

Step 2. Calculate f-5π6.

f-5蟺6=sin-5蟺6=-12

03

Step 3. Now, find g-1f-5π6.

g-1f-5蟺6=g-1-12Let,g-1-12=xg(x)=-12cosx=-12since,cosx=-12forx=2蟺3ontheinterval0鈮�x鈮�蟺.So,g-1f-5蟺6=x=2蟺3

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