Step 1 :

Definition :

The derivative of a function f  with respect to x is denoted by .

  if this limit exists.

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Step 2 :

(a) The function is .

Find :

The derivative of a function.

Multiply numerator and denominator by . \ \

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Substitute the limit.

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Step 3 : \ \

(b) The inverse function is

The domain of a function is all values of , those makes the function mathematically correct.

The denominator of the function should not be zero and square root should not be negative number. \ \

. \ \

.

The domain of the inverse function is . \ \

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Solution :

The domain of the inverse function is .