Q. 105.0( 1 Vote )

If and g(x) = x2 + 1 be two real functions, then find fog and gof.

Answer :

f(x) = , g(x) = x2 + 1


Now,


Domain of f = [ – 3, ∞], domain of g = (– ∞, ∞)


Range of f = [0, ∞), range of g = [1, ∞)


Then, range of f Domain of g and range of g Domain of f


Hence, fog and gof exists


Now,


fog(x) = f(g(x)) = f(x2 + 1)


fog(x) =


Again,


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


gof(x) =


gof(x) = x + 4


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