Functions f(g(x)) for f(x) = x^3 + 5, g(x) = x^2 - 2

[R5232]

I have basic calculus functions problem. I understand the basic concept of functions, but for some reason this problem is not working out to the correct answer.

f(g(x))

f(x)=x³+5
g(x)=x²-2

My understanding of it is as follows:

f(g(x))= (x²-2)³+5

I believe I am correct up to this point. When ever I expand the cubed expression within the parenthesis, I come up short to the correct answer.
Thank you in advance

 

[skeeter]

Re: Functions f(g(x))

I have basic calculus functions problem. I understand the basic concept of functions, but for some reason this problem is not working out to the correct answer.

f(g(x))

f(x)=x³+5
g(x)=x²-2

My understanding of it is as follows:

f(g(x))= (x²-2)³+5

I believe I am correct up to this point. When ever I expand the cubed expression within the parenthesis, I come up short to the correct answer.
Thank you in advance

you are correct ... what did you get when you expanded (x[sup:11ylatfo]2[/sup:11ylatfo] - 2)[sup:11ylatfo]3[/sup:11ylatfo] + 5 ???

maybe whoever wrote the "correct answer" screwed up and not you.

 

[R5232]

Re: Functions f(g(x))

When I worked on expanding the cubed section of the problem, I got an answer which was different.

I used this rule:
x³+y³=(x+y)(x²-xy+y²)
And I applied it to this:
(x²-2)³+5

(x²+2)(x^4-2x²+4)
Which I changed into:
x^6-2x^4+4x²+2x^4-4x²+8
I broke this down to
x^6+13

The answer in the book is : x^5-2x³+5x²+10

I think I might be forgetting a rule, or I may not be applying it correctly.

 

[skeeter]

Re: Functions f(g(x))

wrong rule ... your mistake was starting with x[sup:n0gfwn0j]3[/sup:n0gfwn0j] + y[sup:n0gfwn0j]3[/sup:n0gfwn0j]

cube binomial expansion is ...

(a + b)[sup:n0gfwn0j]3[/sup:n0gfwn0j] = a[sup:n0gfwn0j]3[/sup:n0gfwn0j] + 3a[sup:n0gfwn0j]2[/sup:n0gfwn0j]b + 3ab[sup:n0gfwn0j]2[/sup:n0gfwn0j] + b[sup:n0gfwn0j]3[/sup:n0gfwn0j]

a = x[sup:n0gfwn0j]2[/sup:n0gfwn0j]
b = -2

(x[sup:n0gfwn0j]2[/sup:n0gfwn0j] - 2)[sup:n0gfwn0j]3[/sup:n0gfwn0j] = (x[sup:n0gfwn0j]2[/sup:n0gfwn0j])[sup:n0gfwn0j]3[/sup:n0gfwn0j] + 3(x[sup:n0gfwn0j]2[/sup:n0gfwn0j])[sup:n0gfwn0j]2[/sup:n0gfwn0j](-2) + 3(x[sup:n0gfwn0j]2[/sup:n0gfwn0j])(-2)[sup:n0gfwn0j]2[/sup:n0gfwn0j] + (-2)[sup:n0gfwn0j]3[/sup:n0gfwn0j]

simplify the above, then don't forget to add the 5.