F(x)=log(x+√(x^2+1))

Name: Problem 157, Chapter 1: Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced
Uploaded: 2022-02-26T18:26:51-08:00
Duration: 1 min 36 s
Channel: Varsha Aggarwal
Description: f(x)=log(x+√(x^2+1))

Key Concepts

Logarithmic Functions

Logarithmic functions are the inverse of exponential functions. They transform multiplicative relationships into additive ones and are defined only for positive arguments. Understanding their properties, such as the domain restrictions and the laws of logarithms, is crucial when dealing with expressions that involve logarithms.

Radical Functions

Radical functions involve roots, most commonly square roots, and they require the radicand (the expression inside the radical) to be non-negative for real outputs. Examining the structure of radical expressions is important for determining the domain and ensuring the function produces real numbers.

Composite Functions

Composite functions are created when one function is applied to the result of another function. In the given expression, a logarithmic function is composed with a radical and linear function. Understanding composition is essential for analyzing the overall behavior, domain, and range of complex functions.

Inverse Hyperbolic Functions

Inverse hyperbolic functions, such as the inverse hyperbolic sine, provide a way to express certain combinations of logarithmic and radical functions in a more compact form. Recognizing that expressions like 'log(x + sqrt(x^2+1))' are equivalent to inverse hyperbolic sine can simplify analysis and computations by allowing the use of known identities and properties.

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