Question

the sum of all the integers which are in domain of function f(x) = √[x]-1 + √4-[x] (where [.] denotes the greatest integer function ) will be​

Answer 1

Answer:

Given function f(x)=4−x2[x]+2−−−−√, is define if

4−x2[x]+2≥0

⇒x2−4[x]+2≤0

So, either x2−4≤0

and [x]+2>0 ...(i)

or x2−4≥0

and [x]+2<0 ...(ii)

From Eq. (i),

x∈[−2,2] and x∈[−1,∞)

So, x∈[−1,2] ...(iii)

From Eq. (ii).

x∈(−∞,−2]∪[−2,−∞] and x∈(−∞,−2)

So, x∈(−∞,−2) ...(iv)

From intervals Eqs. (iii) and (iv),

x∈(−∞,−2)∪[−1,2]

Explanation:

hope it helps you...

please mark me as a brainlist!