The correct answer is (x+ 3)3/2 .
The given equation is f(x)= 2/3 x-3
let y = f(x)
we have to find the inverse function
i.e. , express x in terms of y
then, y = f(x)=2/3 x-3
⇒ y = 2/3 x-3
⇒ 2/3 x = y + 3
⇒ x = (y + 3)3/2
Now putting y = f(x)
⇒ x = (f(x) + 3)3/2
Hence , the answer is (x+ 3)3/2 .
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