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.

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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