Question

given: f(x) = 1/x, g(x) = square root of x,

find g(f(x)) and the domain g(f(x))

Answer 1

g(f(x)) = 1/sqrt(x) now looking at this first you know x cannot be negative because the square root of a negative number is not possible unless you are thinking of imaginary numbers and next you see that since x is in the denominator and 1/0 is not possible than you know that x cannot be 0 either therefore the domain for this function is x > 0

Answer 2

would it be correct to write the domain as:
0 < x < infinity

Answer 3

no that would be the same as 0 < x so its more specific

Answer 4

what is the difference between 0 < x and x >0. Is there a difference in the meaning?

Answer 5

no, one means 0 is less than x and the other means x is greater than 0 so they are the exact same thing

Answer 6

thank you.

Answer 7

no prob