Home
Class 12
MATHS
If f : R rarr R and g : R rarr R be two ...

If `f : R rarr R and g : R rarr R` be two mapping such that f(x) = sin x and g(x) = `x^(2)`, then
find the values of (fog) `(sqrt(pi))/(2) "and (gof)"((pi)/(3))`.

Text Solution

Verified by Experts

From Eq. (i), (fog) `x = sin x^(2)`
`therefore ("fog")(sqrt(pi))/(2)=sin.(pi)/(4)=(1)/(sqrt(2))`
and from Eq. (ii), (gof) x = `sin^(2)` x
`therefore (gof)(pi)/(3)=sin^(2).(pi)/(3)=((sqrt(3))/(2))^(2)=(3)/(4)`
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 (fog)(1/2) - (gof) (1/2)

If f(x)= [x], g (x) = abs(x) , then find the value of (fog) (5/2) - (gof)(-5/2)

If f, g : R rarr R such that : f (x) = sqrt x , g (x) = x^2 -1 then find fog and gof.

Find gof and fog if f: RrarrR and g: R rarr R are given by f(x) = cos x and g (x) =3x^2 Show that gof ne fog

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 .

Let f(x) = 2x^2 and g(x) = 3x - 4, x in R . Find the following : fog(x)

If f, g : R rarr R such that : f (x) = x^2 , g (x) = x + 1, then find fog and gof.

Let f: Rrarr R and g: RrarrR be defined by f(x) = x^2 and g(x) = x + 1 . show that gof is not equal to fog .

Let f(x) = 2x^2 and g (x) = 3x - 4 , x in R . Find gof