Question

If f(x) = radical2-x and g(x) = x-1 then find the domain of h(x) = f(x)÷g(x).

Answer 1

Domain → (-∞, 1) ∪ (1, 2]

Step-by-step explanation:

Given functions are,

f(x) =
`√(2-x)`

g(x) = (x - 1)

Since, h(x) =
`(f(x))/(g(x))`

Therefore, h(x) =
`(√(2-x))/((x-1))`

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]