Question

What are the domains of the following expressions:

a)
`15-√(x+2)`
b)
`√(-14(7-2x))`
c)
`(5)/(√(5-x))`
d)
`√(13-(13-2x))`
I know that this is hard but if you answer all of them it is worth 40 points. Thanks!!!

Answer 1

a) x ≥ -2

b) x ≥ 7/2

c) x < 5

d) x ≥ 0

Explanation:

The argument of the square root function cannot be negative, and the denominator of a fraction cannot be zero. Any values of x that satisfy these criteria are part of the domain.

a) x ≥ -2 . . . . the radical content cannot be negative

b) x ≥ 7/2 . . . . simplifies to √(14(2x-7)), so 2x ≥ 7 ⇒ x ≥ 7/2

c) x < 5 . . . . x cannot be 5, but must be less for the root to exist

d) x ≥ 0 . . . . simplifies to √(2x)