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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
The number under a square root sign must be Non negative
(a)
(1) The domain of f ⇒⇒⇒ R - {2}
Because ⇒⇒⇒ x - 2 = 0 ⇒⇒⇒ x = 2
(2) The domain of g ⇒⇒⇒ [1,∞)
Because: x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(3)
The domain of (f+g) ⇒⇒⇒ [1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(4)
The domain of (f-g) ⇒⇒⇒ [1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(5)
The domain of (f*g) ⇒⇒⇒ [1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(6)
The domain of ff ⇒⇒⇒ R - {2}
Because ⇒⇒⇒ x-2 = 0 ⇒⇒⇒ x = 2
(7)
The domain of (f/g) ⇒⇒⇒ (1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 > 0 ⇒⇒⇒ x > 1
(8)
The domain of (g/f) ⇒⇒⇒ [1,∞) - {2}
Because: x - 2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
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(b)
(9)
(10)
(11)
(12)
(13)
(14)
For the given function :
The denominator of a fraction cannot be zero
The number under a square root sign must be Non negative
(a)
(1) The domain of f ⇒⇒⇒ R - {2}
Because ⇒⇒⇒ x - 2 = 0 ⇒⇒⇒ x = 2
(2) The domain of g ⇒⇒⇒ [1,∞)
Because: x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(3)
The domain of (f+g) ⇒⇒⇒ [1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(4)
The domain of (f-g) ⇒⇒⇒ [1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(5)
The domain of (f*g) ⇒⇒⇒ [1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
(6)
The domain of ff ⇒⇒⇒ R - {2}
Because ⇒⇒⇒ x-2 = 0 ⇒⇒⇒ x = 2
(7)
The domain of (f/g) ⇒⇒⇒ (1,∞) - {2}
because: x-2 = 0 ⇒⇒⇒ x = 2 and x - 1 > 0 ⇒⇒⇒ x > 1
(8)
The domain of (g/f) ⇒⇒⇒ [1,∞) - {2}
Because: x - 2 = 0 ⇒⇒⇒ x = 2 and x - 1 ≥ 0 ⇒⇒⇒ x ≥ 1
===================================================
(b)
(9)
(10)
(11)
(12)
(13)
(14)