f(x)={ x^2 : x ≥ 0 x : x<0 . and g(x)=-|x|, x ∈R

Name: Problem 141, Chapter 1: Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced
Uploaded: 2022-03-01T03:22:23-08:00
Duration: 3 min 2 s
Channel: Sahil Kumar
Description: f(x)={ x^2 : x ≥ 0 x : x<0 . and g(x)=-|x|, x ∈R

F(x)={ x^2 : x ≥ 0 x : x<0 . and g(x)=-|x|,...

Key Concepts

Piecewise Function

A piecewise function is defined by different expressions for different parts of its domain. This allows the function to model behaviors that change depending on the input value, which is essential when a single formula cannot describe the phenomenon across the entire domain.

Absolute Value Function

The absolute value function returns the non-negative value of any real number, effectively measuring its distance from zero on the number line regardless of sign. This concept is fundamental in many areas of mathematics, especially in contexts involving distance and magnitude.

Function Transformation

Function transformation involves modifying a basic function through operations such as scaling, reflecting, translating, or compressing. In the context of this problem, applying a negation to the absolute value function reflects its graph over the horizontal axis, altering its range and overall behavior.

Transcript

00:01 Hi guys, so we have this problem in which we need to find out the fog x and the f x is given to us f x is equal to this is x square and x for x squared than equal to 0 and this is x less than 0 and similarly we have a g x which is what this is minus modulus of x you can define this function as well that is what i can write this thing as what minus x for x than equal to 0 and x for what x less than 0 then i can easily find out f of g x so fog x can be given as now this i can write this thing as that minus x will be here so that is what minus x square again i will say what here minus x okay then what we can say here that minus x greater than equal to 0 intersection x got than equal to 0 as well as here i will say what minus x less than 0 intersection x squared than equal to 0 now again we are talking about this function that is what for x so x square this x got than equal to 0 intersection x less than 0 again we have what x now x is what we have we have x less than zero intersection x less than 0 so as you can see if you solve further now this becomes x square but here is what it can be solved as x less than equal to 0 and this is greater than equal to 0 so you have only one number which is what 0 so i can say that this will be minus x square for what x is equal to 0 again here here we get what i can say this kind of thing is equal to what since it is multiply with what minus negative sign so it will be what x greater than 0 intersection with x greater than equal to 0 so that you get x greater than 0 again here we have only what x greater than equal to 0 and x less than 0 so you can say here you'll get what 5 okay you get what 5 here you get x belongs to 5 and here c it will be also x less than so i can say what? that fog x is what? x squared we have a minus x and x.

02:49 X square foot x is equal to 0 and this is x greater than 0 and x less than 0...

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