Which cube root function is always decreasing as x increases?

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Question:

Which cube root function is always decreasing as x increases?

A) f(x) = 3√x-8
B) f(x) = 3√x-5
C) f(x) = 3√-(5-x)
D) f(x) = -3√x+5

Answer:

We know

is an increasing function as when the value of x increases the value of y increases

And when the value of x decreases , the value of y also decreases.

Now if we have (x+a) or (x-a) instead of x, the function shall have a horizontal shift.

So it shall either move left or right but shall not flip.

So

and

are increasing functions.

Only when x becomes -x, that the function shall flip & shall become a decreasing function.

But then it must be – (x-a) or -(x+a) inside.

is also increasing

Only

is a decreasing function.

Option D) is the right answer.

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