Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g compose f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true?

Step-by-step explanation:

Given the function  h(x) = (x – 1)³ + 10 so that h(x) = (g°f)(x). If f(x) = x + a and g(x) = x³ + b, then;

g(f(X)) = g(x+a).

To get g(x+a), we will have to replace the variable x with x+a in g(x) as shown;

g(x+a) =  (x+a)³ + b

g(f(x)) =  (x+a)³ + b

Since h(x)= g(f(x)) = (x – 1)³ + 10

g(f(x)) = (x+a)³ + b = (x – 1)³ + 10

Hence  (x+a)³ + b = (x – 1)³ + 10

On comparing the coefficients to get the value of a and b;

(x+a)³  = (x-1)³

Take the cube root of both sides

∛(x+a)³  = ∛(x-1)³

x+a = x-1

x+a-x = -1

a = -1

Also on comparing, b = 10

Hence the values of a and b would make the composition true are -1 and 10 respectively.

answer: c.  

step-by-step explanation:

mixtures containing substances that get attracted to magnet can be separated using a magnet. we can separate iron from a mixture of sand and iron, as only iron attracts to the magnet.