Q8 of 215 Page 3

If and g(x) = logex are two real functions, then describe functions fog and gof.

f(x) = , g(x) = log e x


Domain of f and g are R.


Range of f= (– ∞, 1) Range of g = (0, e)


Range of f ⊂ Domain of g ⇒ gof exists


Range of g ⊂ Domain f ⇒ fog exists


∴ gof (x) = g(f(x)) = g


∴ gof (x) =


Again


fog (x) = f(g(x)) = f(log e x)


fog (x) =


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