Question

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? a = b =

Answer 1

a: -1

b: 10

edge 2020

Answer 2

a = -1 and

b = 10

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
`x` with
`f(x)` in the function
`g(x)`.

We know that:

`g(x) =x^3+b` and

`f(x) = x + a`

Let us find (g compose f)(x) by replacing
`x` with
`x+a`

`(g\ compose\ f)(x) = (x+a)^3+b`

Also, h(x) = (g compose f)(x) = (x – 1)³ + 10

Therefore,

`(x - 1)^3 + 10 = (x+a)^3+b`

Comparing the corresponding elements of the above expressions:

we get a = -1 and

b = 10