#### To determine

If the given statement is true ot false.

#### Answer

False.

#### Explanation

**Given:**

If f is one-to-one and differentiable with domain ℝ, then (f−1)′(6)=1f′(6).

If f(x1)=f(x2) then function f is one-to-one function.

y=f−1(x) if x=f(y)

Using implicit differentiation, differentiate x=f(y) with respect to *x* to obtain:

1=f′(y)dydx or

1f′(y)=dydx or

1f′(y)=(f−1)(x) or

1f′(f−1(x))=(f−1)′(x)

Hence, the correct statement would be: If f is one to one and differentiable with domain ℝ, then (f−1)′(6)=1f′(f−1(6))

**Conclusion:** Hence, the given statement is false.