Find the domains of f(x)=sin^-1((1-|x|)/(2))+((e^x-1)/(e^x+1))+2015

Name: Problem 129, Chapter 1: Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced
Uploaded: 2022-02-26T15:14:34-08:00
Duration: 1 min 22 s
Channel: Varsha Aggarwal
Description: Find the domains of f(x)=sin^-1((1-|x|)/(2))+((e^x-1)/(e^x+1))+2015

step 1 So here, sine inverse 1 minus mode x by 2 is defined for, is defined for, defined for 1 minus mo

Find the domains of...

Key Concepts

Solving Compound Inequalities for Domain Determination

Many domain problems involve setting up and solving compound inequalities to combine the restrictions imposed by each component of the function. This process usually involves isolating the variable, managing absolute values, and ensuring that all parts of the composite expression satisfy their individual domain requirements. Mastery of compound inequalities is essential for accurately determining the set of all permissible inputs for a function.

Properties of Exponential Functions in Domain Analysis

Exponential functions, such as e^x, are defined for all real numbers. However, when these functions appear in a fraction or composite expression, it is important to check that the operations performed (such as division) do not introduce further constraints like division by zero. In cases where the exponential function appears in both the numerator and denominator, its inherent domain of all real numbers typically remains unchanged.

Domain of Inverse Trigonometric Functions

Inverse trigonometric functions, such as arcsin, have restricted domains for their inputs. Specifically, arcsin is only defined when its argument is within the interval [-1, 1]. This requirement is fundamental when finding the domain of any function that involves inverse trigonometric expressions, as it dictates the values for which the function output is real and valid.

Handling Absolute Value in Domain Restrictions

Absolute value functions serve to convert any real input into a non-negative output and thus influence the domain of composite functions. When combined with other expressions or functions that have input restrictions, it becomes necessary to carefully set up and solve inequalities that incorporate the absolute value, ensuring that the resultant values fall within the permitted range.

Please give Ace some feedback