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

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 $x$ 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

Answer 2

Answer:

a: -1

b: 10

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