Question

$if \: f(x) = x - 1 \: g(x) = x(cube)x \leqslant 0 \: which \: of \: the \: following \: could \: not \: be \: in \: the \: range \: of \: f(g(x))$

Answer 1

$f(x) = x - 1 \\ g(x) = {x}^{3} \\ f(g(x)) = {x}^{3} - 1 \\ x \leqslant 0 \\ see \: the \: graph$
$when \: x = 0 \\ f(g(x)) = - 1 \\ and \: then \: graph \: decreases \: to \: \\ - \infty \\ hence \: range \: is \: ( - 1 \: to \: - \infty )$



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