Home
Class 12
MATHS
Let the function f: RR rarr RR and g: RR...

Let the function `f: RR rarr RR and g: RR rarr RR` be defined by, `f(x) =x^(2)-4x+3 and g(x)=3x-2`. Find formulas which define the composite functions
(i) f o f (ii) g o g (iii) f o g and (iv) g o f

Text Solution

Verified by Experts

The correct Answer is:
(i) `=x^(4)-8x^(3)+18x^(2)-8x` for all `x in RR` (ii) `=9x-8,` for all `x in RR` (iii)`=9x^(2)-24x+15 `, for all `x in RR` (iv) `=3x^(2)-12x+7`, for all `x in RR`
Promotional Banner

Topper's Solved these Questions

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A|12 Videos

  • MAPPING OR FUNCTION

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( very short answer type questions)|22 Videos

  • LOGARITHM

    CHHAYA PUBLICATION|Exercise Long Answer Type Question|12 Videos

  • MATHEMATICAL REASONING

    CHHAYA PUBLICATION|Exercise JEE Main (AIEEE) Archive (2016 )|1 Videos

Similar Questions

Explore conceptually related problems

Let f: RR rarr RR and g: RR rarr RR be two mapping defined by f(x)=x^(2)+3x+1 and g(x)=2x-3 . Find formulas which define the composite mappings (i) (f o f), (ii)(g o g), (iii) (g o f) , (iv) ( f o g)

Let the function f:RR rarr RR and g: RR rarr RR be defined by f(x)=x^(2) and g(x)=x+3, evaluate (f o g) (2) , (ii) (g o f) (3)

Let the functions f: RR rarr RR and g: RR rarr RR be defined by f(x)=x+1 and g(x)=x-1 Prove that , (g o f)=(f o g)=I_(RR)

Let the function f:RR rarr RR and g:RR be defined by f(x) = sin x and g(x)=x^(2) . Show that, (g o f) ne (f o g) .

let the functions f: RR rarr RR and g: RR rarr RR be defined by f(x)=3x+5 and g(x)=x^(2)-3x+2 . Find (i)(g o f) (x^(2)-1), (ii) (f o g )(x+2)

Let f:RR rarr RR and g: RR rarr RR be two mapping defined by f(x)=2x+1 and g(x)=x^(2)-2 , find (g o f) and (f o g).

Let the functions f: RR rarr RR and g: RR rarr RR be given by f(x)=3x-2 and g(x)=3|x|-x^(2) . Find (i) (g o f) (-1) , (ii) (f o g) (-2) , (iii) (g o f) (3), (iv) ( f o g) (4)

Let RR be the set of real numbers and f: RR rarr RR be defined by , f(x) =x^(3) +1 , find f^(-1)(x)

Let RR be the set of real numbers and f: RR rarr RR, g: RR rarr RR, h: RR rarr RR be defined by , f(x) =sin x, g(x)=3x -1, h(x)=x^(2)-4 .Find the formula which defines the product function h o (g o f) and hence compute [h o( g o f)] ((pi)/(2))

Let RR be the set of real numbers and the mapping f: RR rarr RR and g: RR rarr RR be defined by f(x)=5-x^(2) and g(x) =3x -4 , state which of the following is the value of (f o g) (-1) ?