Answer:
a = -1 and
b = 10
Step-by-step explanation:
Given:
h(x) = (x – 1)³ + 10
h(x) = (g compose f)(x).
f(x) = x + a and
g(x) = x³ + b
To find:
The values of a and b = ?
Solution:
First of all, let us have a look at the composite functions.
(g compose f)(x) means we replace the value of [tex]x[/tex] with [tex]f(x)[/tex] in the function [tex]g(x)[/tex].
We know that:
[tex]g(x) =x^3+b[/tex] and
[tex]f(x) = x + a[/tex]
Let us find (g compose f)(x) by replacing [tex]x[/tex] with [tex]x+a[/tex]
[tex](g\ compose\ f)(x) = (x+a)^3+b[/tex]
Also, h(x) = (g compose f)(x) = (x – 1)³ + 10
Therefore,
[tex](x - 1)^3 + 10 = (x+a)^3+b[/tex]
Comparing the corresponding elements of the above expressions:
we get a = -1 and
b = 10
