Home
Class 12
MATHS
Identify the type of the functions: f(x)...

Identify the type of the functions: `f(x)={g(x)-g(-x)}^(3)`

A

Odd

B

Even

C

Neither

D

Both

Text Solution

AI Generated Solution

The correct Answer is:
To identify the type of the function \( f(x) = (g(x) - g(-x))^3 \), we will follow these steps: ### Step 1: Calculate \( f(-x) \) We start by substituting \(-x\) into the function: \[ f(-x) = (g(-x) - g(-(-x)))^3 \] This simplifies to: \[ f(-x) = (g(-x) - g(x))^3 \] ### Step 2: Rearranging the expression Notice that \( g(-x) - g(x) \) can be rewritten as: \[ f(-x) = -(g(x) - g(-x))^3 \] This is because \( g(-x) - g(x) = - (g(x) - g(-x)) \). ### Step 3: Relate \( f(-x) \) to \( f(x) \) Now we can express \( f(-x) \) in terms of \( f(x) \): \[ f(-x) = - (g(x) - g(-x))^3 = -f(x) \] ### Step 4: Conclusion about the function type From the relationship \( f(-x) = -f(x) \), we conclude that the function \( f(x) \) is an **odd function**. ### Summary Thus, the function \( f(x) = (g(x) - g(-x))^3 \) is an odd function. ---
To identify the type of the function \( f(x) = (g(x) - g(-x))^3 \), we will follow these steps: ### Step 1: Calculate \( f(-x) \) We start by substituting \(-x\) into the function: \[ f(-x) = (g(-x) - g(-(-x)))^3 \] ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.11|7 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.12|9 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.9|13 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

v) What type of function is y=f(x)/g(x) ?

Identify the following functions : f(x)=xg(x)g(-x)+"tan"(sinx)

Let f (x), g(x) be two real valued functions then the function h(x) =2 max {f(x)-g(x), 0} is equal to :

Suppose that the function f(x) and g(x) satisfy the system of equations f(x)+3g(x)=x^(2)+x+6 and 2f(x)+4g(x)=2x^(2)+4 for every x. The value of x for which f(x)=g(x) can be equal to

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of f(x)=f(x)g(x/5)-g(x)f(x/3) is

If f(x)=cosx and g(x)=2x+1 , which of the following are even functions? I. f(x)*g(x) II f(g(x)) III. g(f(x))

f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The domain of the function sqrt((f(x))/(g(x))) is

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

Identify the following functions whether odd or even or neither: f(x) = {g(x) - g( - x)}