Answer:
The correct options are B, C and D.
Step-by-step explanation:
The given function is
[tex]f(x)=-\sqrt[3]{x}[/tex]
Using graphing calculator draw the graph of given function.
From the given graph it is clear that:
1. The function is always decreasing. Option A is incorrect.
2. The function is defined for all values of x. So, domain of the function is all real numbers. Option B is correct.
3. [tex]f(x)\rightarrow \infty \text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow -\infty \text{ as }x\rightarrow \infty[/tex]
The output value of the function can be all real number. So, range of the function is all real number.
Range = { y | -∞ < y < ∞}
Option C is correct.
4. If f(x)=-g(x) then f(x) and g(x) are reflection of each other along x axis.
The given function is a reflection of y=³√x. Option D is correct.
5. At x=3,
[tex]f(3)=-\sqrt[3]{3}\neq -27[/tex]
Option E is correct.
Therefore the correct options are B, C and D.
