Target Mathematics

1.13: Range, inverse and composite with square root

0606/13/M/J/16 — Question 6 · 9 marks

The function ff is defined by f(x)=2−x+5f(x) = 2 - \sqrt{x + 5} for −5⩽x<0-5 \leqslant x < 0.
(i)
Write down the range of ff.
[2]
(ii)
Find f−1(x)f^{-1}(x) and state its domain and range.
[4]
(iii)
The function gg is defined by g(x)=4xg(x) = \dfrac{4}{x} for −5⩽x<−1-5 \leqslant x < -1.
Solve fg(x)=0fg(x) = 0.
[3]