Question

3

If f (x) = √2-x and g(x) = x-1, then find the domain of h (x) = f(x) = g(x).
O A.
(-∞0, 1) U (-1,2]
O B.
(-∞0, 1) U (1,2]
O C.
(-∞0, 2) U (1,2]
O D.
(-∞, -1) U (1,2]
O E. (-∞0,-2) U (1,2]
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Answer 1

Answer: B. ( - ∞ , 1 ) U ( 1, 2]

Explanation:

The equation of H(x) is
`(√(2-x) )/(x-1)`

For the bottom denominator, x-1 cannot equal zero

x-1=0

x=1

For the numerator, 2-x square root has to be greater or equal to zero.

`2-x\geq 0`

`x\leq 2`

so the domain is

( - ∞ , 1 ) U ( 1, 2]