Question

f(x) = (x+ 1)³
− (x − 1)
³

represents a function which is

If anyone answers me correctly, I will mark them as the Brainliest​

Answer 1

Answer: YES,  f (x)  is  a function.

Step-by-step explanation:

f ( x ) =  $(x+1)^{3} - (x-1)^{3}$

$[x^{3} +1^{3} +3*x*1(x+1) ] - [ x^{3} -1^{3} -3*x*1(x-1)]\\\\x^{3} -x^{3}+1+1+3x^{2} +3x^{2} +3x-3x\\\\6x^{2} +2$

.: f (x) = $6x^{2} +2$

It is a function as it is continuous and also differentiable and it doesn't fail the vertical line test.

Answer 2

(x+1)^3_(x-1)^3

identity used (a+b)^3=a^3+b^3+3ab (a+b)

(a-b)^3=a^3-b^3-3ab (a+b)

now,

x^3+1+3x (x+1)-(x^3-1-3x (x-1))

x^3+1+3x^2+3x-(x^3-1-3x^2+3x)

x^3+1+3x^2+3x-x^3+1+3x^2-3x

6x^2+2