F (x) = 2-x^1/2 g (x) = x^2-9 what is the domain of g (x) : f (x)

See the domains of each

then find any restricted values (division by 0 and square root by negatives are not allowed)

f (x) = 2 - (x^1/2) or f (x) = 2-√x

g (x) = x²-9

alright

the see the domains of each

domain is numbers you can use

domain of f (x) is all numbers greater than or equal to 0

domain of g (x) is all real numbers

domain of g (x) / f (x)

the denom can't be equal to 0

so f (x) = 0 is restricted value

solve f (x) = 2-√x=0

2-√x=0

2=√x

4=x

so x can't be 4 either

domain is real numbers greater than or equal to 0 not including 4

in interval notation it is [0,4) U (4,+∞)