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3 years ago

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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?

2 answers:

lina2011 [118]3 years ago

8 0

Answer:

a: -1

b: 10

edge 2020

Amiraneli [1.4K]3 years ago

5 0

Answer:

<h2>a = -1, b = 10</h2>

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

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

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