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Find the inverse function of the following=
f(x)=2∙3x+9x

  1.   log3⁡((√(x+1))+1)
  2.   log3⁡((√(x+1))-1)
  3.   log3⁡((√(x-1))+1)
  4.   log3⁡((√(x+1))-2)
asked in Calculus by Veteran (11.1k points)   | 90 views
can someone solve this using Log??

1 Answer

+3 votes
Best answer

Let 3 = t and f(x) = y, then the given function can be rewritten as :

       y = 2t + t2

⇒    y =  t2  + 2t + 1  - 1

⇒    y =  (t + 1)2 - 1

⇒    (t + 1)2  =  1 + y

⇒    t   =  √ (y + 1) - 1

⇒   3x  =  √ (y + 1) - 1

Now taking log both sides , we have :

⇒   x   =  log3(√ (y + 1) - 1)

Hence now to find inverse , we swap x and y , 

⇒   y   =  log3((√ (x + 1) ) - 1)

 

Hence 2) is the correct answer..

 

answered by Veteran (65k points)  
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