Q. 95.0( 1 Vote )

If f: R and g: [1, 1] R be defined as f(x) = tan x and respectively. Describe fog and gof.

Answer :

f: and g: [ – 1,1]R defined as f(x) = tan x and g(x) =


Range of f: let y = f(x)


y = tan x


x = tan – 1 y


Since, x ϵ , y ϵ (– ∞, ∞)


As Range of f Domain of g


gof exists.


Similarly, let y = g(x)


y =


x =


Range of g is [ – 1,1]


As, Range of g Domain of f


Hence, fog also exists


Now,


fog(x) = f(g(x)) = f


fog(x) = tan


Again,


gof(x) = g(f(x)) = g(tan x)


gof(x) =


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