Question

Answer the following:

Find the range of the following function.

f(x) = `1/(1 + sqrt(x))`

Answer 1

f(x) = `1/(1 + sqrt(x))` = y, (say)

∴ `sqrt(x)  y + y` = 1

∴ `sqrt(x) = (1 - y)/y ≥ 0` 

∴ `(y - 1)/y ≤ 0`

∴ 0 < y ≤ 1

Range = (0, 1]