Question

Find the domain and the range of the real function, `f(x)=(1)/sqrt(x-2)`

Answer 1

We have, `f(x)=(1)/sqrt(x-2)`
Clearly, f(x) defined for all real values of x for which `x-2gt0`, i.e., `xgt2`.
`:."dom "(f)=(2,oo)`.
For any real value of `xgt2`, we have
`xgt2impliesx-2gt0impliessqrt(x-2)gt0`
`implies(1)/(sqrt(x-2))gt0impliesf(x)gt0`.
`:."range "(f)=(0,oo)`.
Hence, dom `(f)=(2,oo)"and range "(f)=(0,oo)`.