Question

3. The functions f and g are defined by
$f(x) = \frac{8}{x - 2} + 2 \: for \: x > 2$

$g(x) = \frac{8}{x - 2} + 2 \: for \: 2 < x < 4$
(a)(i) State the range of the function f.
(ii) State the range of the function g.
(iii) State the range of the function fg.
(b) Explain why the function gf cannot be formed.​

Answer 1

i) range is (-infinity,2)
ii) range is (6, infinity)
iii) range is (6,infinity)
b)
Cause the range of f doesn’t match any element of the domain of g