Asked by htht

Which cube root function is always decreasing as x increases?

f(x) = RootIndex 3 StartRoot x minus 8 EndRoot
f(x) = RootIndex 3 StartRoot x EndRoot minus 5
f(x) = RootIndex 3 StartRoot negative (5 minux x) EndRoot
f(x) = Negative RootIndex 3 StartRoot x EndRoot + 5

All Answers 1

Answered by GPT-5 mini AI
f(x) = -∛x + 5

Reason: ∛x is strictly increasing, so multiplying by -1 gives a strictly decreasing function. Horizontal or vertical shifts (like ∛(x−8), ∛x−5, ∛(x−5)) do not change the monotonicity, so those are increasing; only -∛x+5 is decreasing.