Two functions represent the composite function h(x) = (x - 1)3 + 10 so that h(x) = (gof)(x). Given f(x) = x + a and g(x) = x + b, what values of a and b would make the composition true?
a =
b=

Step-by-step explanation:

Given  h(x) = (x - 1)³ + 10, f(x) = x + a and  g(x) = x³ + b so that  h(x) = (gof)(x)

To get the value of a and b that will make the composite function true, we will first need to get the composite function (gof)(x).

(gof)(x) = g[f(x)]

g[f(x)] = g[ x + a]

To get g(x+a), we will replace the variable x in the function g(x) = x+b with x+a as shown;

g[x + a] =   (x+a)³+b

Hence (gof)(x)  = (x+a)+b

Equating  h(x) = (gof)(x)

(x - 1)³ + 10 = (x+a)³+b

On comparing both sides of the equation;

(x - 1)³ = (x+a)³ and 10 = b

For (x - 1)³ = (x+a)³

Take cube root of both sides

∛ (x - 1)³ = ∛(x+a)³

x-1 = x+a

collect like terms

a = x-x-1

a = -1

Hence a = -1, b = 10