YAMT: Pre calc help once more...

[Ricemarine]

Ok, so...

g(x) = 1/(x-2)
k(x) = x^2-2

Solve for (gk)(x), and k(g(x))

Are they similar? Why?...

Now in the first one, I got (x^2-2)/(x-2)
The second one, my teacher I think inverted the composite, giving (g(k(x)), which she gave me the answer of 1/(x^2-4)...


Someone help? . It's confusing...
Thx...

 

[DrPizza]

k(2) means 2^2 - 2
k(3) means 3^2 - 2
k(m) means m^2 - 2

k( ) means ^2 - 2

whatever's in those parenthesis, replaces x in the function.

So, k(g(x)) means [g(x)]^2 - 2
[1/(x-2)]^2 - 2

= 1/(x-2)^2 - 2(x-2)^2/(x-2)^2 (getting a common denominator)

So, (1-2(x-2)^2) / (x-2)^2

First one seems fine.