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

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.

So

is also increasing

Only

is a decreasing function.

Option D) is the right answer.

D.

Step-by-step explanation:

Decreasing function: A function is said to be decreasing function

When

Then,

It is an increasing function because when x increases then the value of f(x) is also increases.

A.

In given function only x- coordinate shift left side .Therefore, the cube root function remain increasing.

B.

It is increasing function because when x increasing then the value of f(x) is also increase.

C.

It is also increasing function because when x increase then the value of function is also increases.

D.

Substitute x=-5

Then we get f(x)=0

Substitute x=-4

Then, we get

Substitute x=-3

Then, we get

When x increases then the value of function decrease.

Hence, the function is decreasing .

Option D is true.

21

step-by-step explanation: