ANSWER
A
[tex]( - \infty , + \infty )
[/tex]
EXPLANATION.
The given function is
[tex]f(x) = 2 {x}^{3} + 21[/tex]
Let
[tex]y= 2 {x}^{3} + 21[/tex]
Solve for x.
[tex]2 {x}^{3} = y - 21[/tex]
[tex] {x}^{3} = \frac{1}{2} y - \frac{21}{2} [/tex]
Take cubic root of both sides,
[tex]x = \sqrt[3]{ \frac{1}{2} y - \frac{21}{2} } [/tex]
x is defined for all real values of y.
The range refers to the values of y, for which x is defined.
Hence the range is all real numbers.
In interval notation, we write this as,
[tex]( - \infty , + \infty )
[/tex]
The correct choice is A.
