Which cube root function is always decreasing as x increases? A) f(x) = 3√x8 B) f(x) = 3√x5 C) f(x) = 3√(5x) D) f(x) = 3√x+5
Question
A) f(x) = 3√x8
B) f(x) = 3√x5
C) f(x) = 3√(5x)
D) f(x) = 3√x+5
2 Answer

1. User Answers zagreb
We know
[tex]y=\sqrt[3]{x}[/tex]
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 (xa) instead of x, the function shall have a horizontal shift.
So it shall either move left or right but shall not flip.
So
[tex]y=\sqrt[3]{(x8)}[/tex] and [tex]y=\sqrt[3]{(x5)}[/tex]
are increasing functions.
Only when x becomes x, that the function shall flip & shall become a decreasing function.
But then it must be  (xa) or (x+a) inside.
So
[tex]y=\sqrt[3]{(5x)}[/tex] is also increasing
Only
[tex]y= \sqrt[3]{(x+5)}[/tex]
is a decreasing function.
Option D) is the right answer.

2. User Answers lublana
Answer:
D.[tex]f(x)=\sqrt[3]{x+5}[/tex]
Stepbystep explanation:
Decreasing function: A function is said to be decreasing function
When [tex]x_1<x_2[/tex]
Then, [tex]f(x_1)>f(x_2)[/tex]
[tex]f(x)=\sqrt[3]{x}[/tex]
It is an increasing function because when x increases then the value of f(x) is also increases.
A.[tex]f(x)=\sqrt[3]{x8}[/tex]
In given function only x coordinate shift left side .Therefore, the cube root function remain increasing.
B.[tex]f(x)=\sqrt[3]{x5}[/tex]
It is increasing function because when x increasing then the value of f(x) is also increase.
C.[tex]f(x)=\sqrt[3]{(5x)}[/tex]
It is also increasing function because when x increase then the value of function is also increases.
D.[tex]f(x)=\sqrt[3]{x+5}[/tex]
Substitute x=5
Then we get f(x)=0
Substitute x=4
Then, we get
[tex]f(4)=\sqrt[3]{4+5}=1[/tex]
Substitute x=3
Then, we get
[tex]f(3)=\sqrt[3]{3+5}=1.26[/tex]
When x increases then the value of function decrease.
Hence, the function is decreasing .
Option D is true.