Home
Class 12
MATHS
If the functions f(x) and g(x) are defin...

If the functions `f(x) and g(x)` are defined on `R -> R` such that `f(x)={0, x in` retional and `x, x in` irrational ; `g(x)={0, x in` irratinal and `x,x in` rational then `(f-g)(x)` is

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the functions \( f(x) \) and \( g(x) \) and then find the expression for \( (f - g)(x) \). ### Step-by-Step Solution: 1. **Define the Functions**: - The function \( f(x) \) is defined as: \[ f(x) = ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.1|15 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Two mappings f:R to R and g:R to R are defined as follows: f(x)={(0,"when x is rational"),(1,"when x is irrational"):} and g(x)={(-1,"wnen x is rational"),(0,"when x is irrational"):} then the value of [(gof)(e)+(fog)(pi)] is -

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, when x is rational and x, when x is irrational then (f-g) is A. one-one and onto B. neither one-one nor onto C. many one and onto D one-one and into

A function g(x) is defined g(x)=2f(x^2/2)+f(6-x^2),AA x in R such f''(x)> 0, AA x in R , then m g(x) has

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

Function f: R to R and g : R to R are defined as f(x)=sin x and g(x) =e^(x) . Find (gof)(x) and (fog)(x).

If f, g : R to R such that f(x) = 3 x^(2) - 2, g (x) = sin (2x) the g of =

If both f(x) & g(x) are differentiable functions at x=x_0 then the function defiend as h(x) =Maximum {f(x), g(x)}

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f(x) and g(x) be defined and differntiable for all x ge x_0 and f(x_0)=g(x_0) f(x) ge (x) for x gt x_0 then