Home
Class 12
MATHS
If f:R -> R, g:R -> R defined as f(x) = ...

If `f:R -> R, g:R -> R` defined as `f(x) = sin x and g(x) = x^2`, then find the value of `(gof)(x) and (fog)(x) `and also prove that `gof != fog`.

Text Solution

Verified by Experts

Let `x in R`
`therefore (fog)x=f{g(x)} " "[because g(x)=x^(2)]`
`=f{x^(2)}=sinx^(2)" ... (i)"`
`[because f(x)=sinx]`
and (gof) `x=g{f(x)}`
`=g(sinx)" "[becausef(x)=sinx]`
`=sin^(2)x" ... (ii)"`
`[because g(x)=x^(2)]`
From Eqs. (i) and (ii), we get (fog) x `ne`(gof)x, `AAx inR` Hence, fog `ne` gof
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|11 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|10 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise The Straight Lines Exercise 8 : (Questions Asked in Previous 13 years Exams)|1 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = [x] and g(x) = |x| then find the value of (gof) (5/3) - (fog) (5/3)

If f(x) = sin x and g(x) = 2x, find fog.

Let f(x) = [x] and g(x) = |x| then find the value of (fog)(1/2) - (gof) (1/2)

Find fog if f(x)= x-2 and g(x) = 3x

If f(x) = (x+1)/(x+2) and g(x) = x^2 , then find fog

Find gof if f(x)= 8x-2 and g(x) = 2x

Find fog if f(x) = |x| and g(x) = |5x-2|

If f(x) = log x and g(x) = e^x then fog(x) is :

If f(x) = (x+1)/(x+2) and g(x) = x^2 , then find gof.