The domain is the set of all possible
x-values which will make the function valid.
For the given function The denominator of a fraction cannot be
zero
(a)(1) The domain of f ⇒⇒⇒ R - {-3}
Because ⇒⇒⇒ x+3 = 0 ⇒⇒⇒ x =-3
(2) The domain of g ⇒⇒⇒ R - {4}
Because: 4 - x = 0 ⇒⇒⇒ x = 4
(3)
The domain of (f+g) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3 and 4 - x = 0 ⇒⇒⇒ x = 4
(4)
The domain of (f-g) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3 and 4 - x = 0 ⇒⇒⇒ x = 4
(5)
The domain of (f*g) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3 and 4 - x = 0 ⇒⇒⇒ x = 4
(6)
The domain of ff ⇒⇒⇒ R - {-3}
Because ⇒⇒⇒ x+3 = 0 ⇒⇒⇒ x =-3
(7)
The domain of (f/g) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3 and 4 - x = 0 ⇒⇒⇒ x = 4
(8)
The domain of (g/f) ⇒⇒⇒ R - {-3,4}
because: x+3 = 0 ⇒⇒⇒ x = -3 and 4 - x = 0 ⇒⇒⇒ x = 4
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(b)
(9)
∴
(10)
∴
(11)
(12)
(13)
(14)
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