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Differentiation of Inverse Function - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • 16 Questions around this concept.

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If f(x)=x^{2}-x+5,x>\frac{1}{2} and g(x) is its inverse function,then  g'(7)   equals:

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Concepts Covered - 1

Differentiation of Inverse Function

Differentiation of Inverse Function

Let f(x) be a function that is both invertible and differentiable. Let y=g(x) be the inverse of f(x). Then,
f(g(x))=x (Property of inverse function)
Differentiating both sides

f′(g(x))⋅g′(x)=1 (Chain Rule) g′(x)=1f′(g(x))

Illustration

If f(x)=x3+x5, and g(x) is the inverse of f(x), then find g′(2)
Solution
Using g′(x)=1f′(g(x)), put x=2

g′(2)=1f′(g(2))
Now we need to get the value of g(2)
As we know for inverse functions if f(a)=b, then g(b)=a. So let g(2)=p, then f(p)=2

p3+p5=2p=1=g(2)
Putting this in (i)

g′(2)=1f′(1)=1f′(1)=13x2+5x4( at x=1)=18

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Differentiation of Inverse Function

Study other Related Concepts

Differentiation of Inverse Function Current Topic

Limit
Left-Hand Limits and Right-Hand Limits
Algebra of Limits
Limit of Indeterminate Form and Algebraic limit
Limit of Algebraic function
Limit Using Expansion
Sandwich Theorem
Limits of Trigonometric Functions
Exponential and Logarithmic Limits
Limits of the form (1 power infinity)

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