If f(x)=(√(2-x)) and g(x)= (x-1), then find the domain of h(x)=f(x)/g(x) answer is:               ( - ∞ , 1 ) u ( 1 , 2]

The function is . 

The domain can only contain those values of x for which the denominator is not zero, that is all real numbers except 1, 

AND for which 2-x i greater or equal to 0 (because if 2-x is negative, the square root of it cannot be calculated).

The last inequation, , is solved as follows:

adding -2 to both sides we have .

Multiplying by -1 (and not forgetting to swap the sign), we have .

So x must be smaller or equal than 2, but also x cannot be 1, from the first condition. This means that the answer is ( - ∞ , 1 ) U ( 1 , 2].


 ( - ∞ , 1 ) U ( 1 , 2]