Question

Find r(x + 1) if r(x) = x3 + x + 1

Answer 1

Substitute x + 1 as x in the equation of the function:

`r(x)=x^3+x+1\\\\r(x+1)=(x+1)^3+(x+1)+1=x^3+3(x^2)(1)+3(x)(1^2)+1^3+x+1+1\\\\=x^3+3x^2+3x+x+2=x^3+3x^2+4x+2`

Used

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

Answer 2

r(x + 1) = x^3 + 3x^2 + 4x + 3

Explanation:

r(x) = x3 + x + 1

Replace x with x + 1 is r(x) and simplify.

r(x + 1) = (x + 1)^3 + x + 1 + 1

= (x^2 + 2x + 1)(x + 1) + x + 2

= x^3 + x^2 + 2x^2 + 2x + x + 1 + x + 2

r(x + 1) = x^3 + 3x^2 + 4x + 3