Subject: algebra II
Name: Oryan
Who are you: Student

HELP!!! I just don't get it! How do I even go about starting to figure this out! Given f(x)=-2x^3 and g(x)-4x-5, find g(f(-1))

Hi Oryan.

I'll show you how to solve this with a similar question:

f(x) = 3x²-7
g(x) = 5+8x^-1
Find g(f(-1)).

Remember BEDMAS from elementary school? It says do what's in the brackets first, so g(f(-1)) becomes first a question of what is f(-1)?

Plug it in: f(-1) = 3(-1)² - 7 = 3 - 7 = -4.

Now replace f(-1) with -4: g(f(-1)) = g(-4). So what is g(-4)?
Substitute -4 for x in the expression for g(x):

g(-4) = 5 + 8(-4)^-1 = 5 - 8/4 = 3.

There is slightly different approach as well:
in g(x) = 5 + 8x^-1 we are saying that whatever is between the
parentheses on the left hand side replaces x on the right hand side.
This means g(f(x)) = 5+ 8(f(x))^-1.

But we can substitute for f(x) now on the right hand side:

So g(f(x)) = 5 + 8(3x²-7)^-1 = 5 + 8 / (3x² - 7).

And now to solve g(f(-1)) you can substitute -1 for x:

g(f(-1) = 5 + 8 / (3(-1)² - 7) = 5 + 8 / (3 - 7) = 5 + 8 / (-4) = 3.

Hope this helps,
Stephen La Rocque.