Question

find the domain of f(x)=(2-x)^1÷2+(1+x)^1÷2​

Answer 1

Domain of a function, basically, is the set of all those values for which the function doesn't acquire any absurd form.

f(x) = √(2-x) + √(1+x)

For f(x) to be defined:

(2-x) ≥ 0

=> x ≤ 2. .....................(a)

and,

(1+x) ≥ 0

=> x ≥ -1 .....................(b)

from (a) and (b),

-1 ≤ x ≤ 2

Hence, the domain of the given function is: Domain = [-1, 2]