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 [tex]\displaystyle{ \frac{ \sqrt{2-x}}{x-1} [/tex]. 

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, [tex]2-x \geq 0[/tex], is solved as follows:

adding -2 to both sides we have [tex]-x \geq -2[/tex].


Multiplying by -1 (and not forgetting to swap the sign), we have [tex]x \leq 2[/tex].


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].


Answer: ( - ∞ , 1 ) U ( 1 , 2]