algebra 2 help?

Question

Are f and g inverses of each other?
f(x) = (2x + -6)/7
g(x) = (7/2)x + 3

A yes
B no

Answer 1

To figure this out, plug in g(x) wherever you see an x in f(x).

(2*((7/2)x + 3) + -6)/7
((7x + 6) - 6)/7
7x/7
x

The end result of "x" means that you can take any x, shove it through g(x), and then shove the result through f(x), and you'll end up with the same x you started with.

That makes f and g into inverses.

(Technically you'd have to make sure that the process works in reverse too: if you first shove through f(x) and then shove the result through g(x), you should also end up with what you started. However, for simple polynomials like these, if f is the inverse of g then g will necessarily be the inverse of f).

Hope that helps!

Answer 2

yes.

to find out, find the inverse of one equation and if it's the same as teh other then they're inverses.