Answer :

(i) g o f


To find: g o f


Formula used: g o f = g(f(x))


Given: (i) f : R R : f(x) = (2x + 1)


(ii) g : R R : g(x) = (x2 - 2)


Solution: We have,


g o f = g(f(x)) = g(2x + 1) = [ (2x + 1)2 – 2 ]


4x2 + 4x + 1 – 2


4x2 + 4x – 1


Ans). g o f (x) = 4x2 + 4x – 1


(ii) f o g


To find: f o g


Formula used: f o g = f(g(x))


Given: (i) f : R R : f(x) = (2x + 1)


(ii) g : R R : g(x) = (x2 - 2)


Solution: We have,


f o g = f(g(x)) = f(x2 - 2) = [ 2(x2 - 2) + 1 ]


2x2 - 4 + 1


2x2 – 3


Ans). f o g (x) = 2x2 – 3


(iii) f o f


To find: f o f


Formula used: f o f = f(f(x))


Given: (i) f : R R : f(x) = (2x + 1)


Solution: We have,


f o f = f(f(x)) = f(2x + 1) = [ 2(2x + 1) + 1 ]


4x + 2 + 1


4x + 3


Ans). f o f (x) = 4x+ 3


(iv) g o g


To find: g o g


Formula used: g o g = g(g(x))


Given: (i) g : R R : g(x) = (x2 - 2)


Solution: We have,


g o g = g(g(x)) = g(x2 - 2) = [ (x2 - 2)2 – 2]


x4 -4x2 + 4 - 2


x4 -4x2 + 2


Ans). g o g (x) = x4 -4x2 + 2


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