Question

Write the equation of the function g(x) if g(x) = f(x - 3) +1 and f(x) = x3 + 1.

Answer 1

Solution,

f(x) =
`x^(3)` + 1

Put x = x - 3,

f(x - 3) =
`(x-3)^(3)` + 1

Now,

g(x) = f(x - 3) + 1

or, g(x) =[
`(x-3)^(3)` +1 ] + 1

or, g(x) =
`x^(3) -9x^(2) + 27x - 1 + 1+1`

or, g(x) =
`x^(3) - 9x^(2) +27x + 1`