What is the domain of f(x)= (1+sqrt x)^3 and f(x)= 2^x?

Question

im more than a little rusty with this stuff...

Answer 1

1) Unless you're using complex numbers you cannot take the square root of a negative number.  That is the only restriction in this function.

Answer:   {x| x >= 0}

2) There are absolutely no restrictions on this function.  You can raise 2 to any power that you wish.  Here negative values of x are totally acceptable, as    2^-z = 1 / (2^z)

The domain is the entire set of real numbers or {x| x is real}

Answer 2

To find the domain you always have to think where the function is defined and where it is not defined. In fact the domain of a function means to find the set of values where the function is defined.

Considering your function,

                                  f(x) = (1 + sqrtx)^3

Here the value of sqrt x is defined for only non- negative values of x.

Hence the domain is [0, infinity).

                         f(x) = 2^x.

Here f(x) is defined for all values of x. Hence it's domain is the entire set of real numbers R.