Find the domain of f(x) =7+Square root of 3x+21, and express it using interval notation?

Answer 1

f(x) =7+Square root of 3x+21
assuming you mean
f(x) =7+sqrt( 3x+21 )
the domain consists of all the real numbers for which the square root is defined:
3x+21>=0
3x >= -21
x >= -7
so in interval notation:
[-7, infinity)
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Answer 2

.f(x) =7+Square root of 3x+21

f(x) =7+sqrt( 3x+21 )

3x+21>=0
3x >= -21
x >= -7

[-7, infinity)

Answer 3

for function to map into real values

sqrt(3x)>0
=> x>0

x E (0,infinity)
f is a function mapping from real +ve values real +ve values
f(R+)---->R+