Procedure of Finding Inverse of f
- Check for one-one and onto function.
- If invertible then, interchange x and y in definition of f(x).
- Find y in terms of x.
- Obtained y is inverse of f defined from B ⇢ A.
Example: f(x) = ex
y = ex
Inverse of f(x) will be obtained by y ↔ x
x = ey
y = ln x
Now, ex and ln x are inverse function of each other.
Check: Derivative of Sin Inverse x
Derivatives of Inverse Functions
In mathematics, a function(e.g. f), is said to be an inverse of another(e.g. g), if given the output of g returns the input value given to f. Additionally, this must hold true for every element in the domain co-domain(range) of g. E.g. assuming x and y are constants if g(x) = y and f(y) = x then the function f is said to be an inverse of the function g. Or in other words, if a function f : A ⇢ B is one – one and onto function or bijective function, then a function defined by g : B ⇢ A is known as inverse of function f. The inverse function is also known as the anti function. The inverse of function is denoted by f-1.
f(g(x)) = g(f(x)) = x
Here, f and g are inverse functions.
Table of Content
- Overview of Derivatives of Inverse Functions
- Procedure of finding inverse of f
- Derivatives of Inverse Functions
- How to find derivatives of inverse functions from the table?
- Derivatives of Inverse Trigonometric Functions
- How to find the derivatives of inverse trigonometric functions?
- 1. Derivative of f given by f(x) = sin–1 x.
- 2. Derivative of f given by f(x) = cos–1 x.
- 3. Derivative of f given by f(x) = tan–1 x.
- 4. Derivative of f given by f(x) = cot–1 x.
- 5. Derivative of f given by f(x) = sec–1 x.
- 6. Derivative of f given by f(x) = cosec–1 x.
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