Question

got a little composition question..

Answer 1

one sec lemme post it

Answer 2

im trying to find fog

Answer 3

i just got x for all of em

Answer 4

for example, if x<-1, we can write:
\[\large f\left( {g\left( x \right)} \right) = g\left( x \right) + 2 = x - 2 + 2 = ...\]

Answer 5

if \[ - 1 \leqslant x \leqslant 1\]
we have:
\[\large f\left( {g\left( x \right)} \right) = - g\left( x \right) = - \left( { - x} \right) = ...?\]

Answer 6

x

Answer 7

finally, if x>1, we can write:
\[\large f\left( {g\left( x \right)} \right) = g\left( x \right) - 2 = x + 2 - 2 = ...?\]

Answer 8

what do they mean when they say it is easy to verify fog = \[I _{R}\]

Answer 9

since we have:
f(g(x))x
and
g(f(x))=x
we can say that f is the inverse function of g, and that g is the inverse function of f, so we can write:
\[\large \begin{gathered}
f \circ g = {I_R} \hfill \\
g \circ f = {I_R} \hfill \\
\end{gathered} \]

Answer 10

oops.. f(g(x))=x

Answer 11

oh okay

Answer 12

so it was just that simple?

Answer 13

yes!

Answer 14

haha well um thanks :p

Answer 15

thanks :)