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find the inverse

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3 3 votes

Let 3x  = 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..

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