Decomposing A Composite Function...3

[nycmathguy]

Section 1.8
Questions 54 & 56

See attachment.

I need to find the outer and inner functions.

Question 54

The outer function is f(x) = 4/(x^2).

The inner function is g(x) = 5x + 2.

Question 56

I inner function is g(x) = 10 - 27x^3.

Must I factor the numerator to find the outer function f(x)?

 

[MathLover1]

54. correct
56.

f(g(x) )= (27x^3+6x)/(10 - 27x^3)

=> (27x^3+6x)/(10 - 27x^3) this must be g(x)
then f(x )= x

 

[nycmathguy]

54. correct
56.

f(g(x) )= (27x^3+6x)/(10 - 27x^3)

=> (27x^3+6x)/(10 - 27x^3) this must be g(x)
then f(x )= x

Let me see.

You are saying that a (function)/(function) is g(x), the inner function. Then f(x) = x or the line y = x.

Yes?

 

[MathLover1]

Yes

 

[nycmathguy]

Yes

Ok. Let me make up a question.

Say h(x) = 2x/(x - 6).

You are saying that the inner function is 2x/(x - 6).

The outer function is f(x) = x.

Yes?

Prove:

(f ° g)(x) = h(x)

h(x) = f(g(x))

h(x) = f(2x/(x - 6))

h(x) = original function given.

h(x) = 2x/(x - 6)

 

[MathLover1]

yes

 

[nycmathguy]

yes

Ok. Be back later.