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

Step-by-step explanation:

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

The cube root is obtained by reversing the process of finding the cube of a

number, therefore, it can be negative.

Reasons:

The given options;

f(x) = ∛(x - 8)

f(x) = ∛(x) - 5

f(x) = ∛(x) + 5

Required: The cube root that is always decreasing as x increases.

Solution:

∛(x³) = x

Therefore, as x increases, x³ increases, and ∛(x³) = x increases

The analyzing the given options;

f(x) = ∛(x - 8)

In the above option, as x increases, (x - 8) increases, therefore, ∛(x - 8) increases

f(x) = ∛(x) - 5

In the above option, as x increases, ∛(x) increases, therefore, ∛(x) - 5 increases

In the above option, as x increases, (5 - x) decreases, therefore, ∛(5 - x) decreases.

Therefore, the above cube root function is always decreasing as x increases

f(x) = ∛(x) + 5

In the above option, as x increases, ∛(x) increases, therefore, ∛(x) + 5 increases.

The cube root function that is always decreasing as x increases is option;

Learn more about decreasing functions here:

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