Q1 of 215 Page 3

Find fog and gof, if

f(x) = x2 + 2,

f(x) = x2 + 1 and


Range of f = (2,∞) ⊂ Domain of g = R ⇒ gof exists


Range of g= R – [ – 1] ⊂ Domain of f =R ⇒ fog exists


Now,


and




Hence,


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Let f(x) = x2 + x + 1 and g(x) = sin x. Show that fog ≠ gof.

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If f(x) = |x|, prove that fof = f.