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graphs

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i have no idea what im doing..

http://prntscr.com/l7a2x8

Oct 17, 2018

#1
+1

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

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

Oct 17, 2018
#2
+1

where did you get from f(x) = x+1

thank you !

Oct 17, 2018
#4
+1

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

Oct 17, 2018
#5
+2

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

Dimitristhym  Oct 18, 2018