#1**+2 **

Ok we have:

f(x) = x+1 , xΕ [-2,2]

and g(x) = x + 1 , xE [-2,1)

1 , x=2

-x + 3 , xE(1,4]

So f(g(x)) = (x+1) + 1 , xE [-2,1)

(-x + 3) + 1 , xE (1,2]

We need around 1 to know the equation of function f(g(x)) because we want lim x->1

so when lim x -> 1+ f(g(x)) = (x+1) + 1 = 1 + 1 + 1 = 3

when lim x -> 1- f(g(x)) = (-x+3) + 1 = -1 + 3 + 1 = 2 +1 = 3 so

lim x -> 1+ = lim x -> 1- = 3

lim x -> 1 = 3

__Correct answer (C)__

f(x) , g(x) I find the equation of function from graph!

Dimitristhym
Oct 17, 2018

#2

#4**+2 **

Because its a straight so its f(x) = ax + b

and because x,y increase at the same rate its 1 so f(x) = x + b and b = 1 to verify the equation !

Dimitristhym
Oct 18, 2018

#3**+3 **

here is the question

I do not understand Dimitris answer BUT

I also think that the answer is 3

as x tends to 1 g(x) tends to 2

and f(2)=3

Melody
Oct 17, 2018

#5**+3 **

Yes this is the same and this is faster and i think the fastest way to answer!

Dimitristhym
Oct 18, 2018