Question

What is the range of the cubic function f(x)=2x^3+21

Answer 1

ANSWER

A

$( - \infty , + \infty )$

EXPLANATION.

The given function is

$f(x) = 2 {x}^{3} + 21$

Let

$y= 2 {x}^{3} + 21$

Solve for x.

$2 {x}^{3} = y - 21$

${x}^{3} = \frac{1}{2} y - \frac{21}{2}$

Take cubic root of both sides,

$x = \sqrt[3]{ \frac{1}{2} y - \frac{21}{2} }$

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,

$( - \infty , + \infty )$

The correct choice is A.

Answer 2

Answer:

Yes it’s A

Step-by-step explanation: