Answer:
Domain → (-∞, 1) ∪ (1, 2]
Explanation:
Given functions are,
f(x) = [tex]\sqrt{2-x}[/tex]
g(x) = (x - 1)
Since, h(x) = [tex]\frac{f(x)}{g(x)}[/tex]
Therefore, h(x) = [tex]\frac{\sqrt{2-x}}{(x-1)}[/tex]
This function is defined for,
(2 - x) ≥ 0 [Since, square root of negative numbers is not defined]
⇒ x ≤ 2
And (x - 1) ≠ 0 [Since, fraction is not defined for denominator = 0]
x ≠ 1
Therefore, domain of the function 'h' will be,
(-∞, 1) ∪ (1, 2]
