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

Question

Philoid · Accepted Answer

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) =

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