Find fog and gof, if
f(x) = sin–1 x, g(x) = x2
f(x) = sin – 1 x and g (x) = x2
Range of f=
Domain of g = R ⇒ gof exist
Range of g= (0,∞) ⊂ Domain of f = R ⇒ fog exist
Now,
fog (x) = f(g(x)) = f(x2) = sin – 1x2 and
gof(x) = g(f(x)) = g (sin – 1 x) = (sin – 1x)2
Hence, fog(x) = sin – 1x2 and gof(x) = (sin – 1x)2
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