lavalava
use the function to answer the question:
x+14 if x<-7
f(x) 21 if -7 ≤x<-6
x^2 -1 if x ≥ -6
what is the value of f(-6)?
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Eyad
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Since u want to find F(x) at x=-6 ,
U will use the Function F(x)= x^2-1 because x is bigger or **Equal** -6
Plug -6 in the equation so it will be
F(-6)=(-6)^2-1=.....
lavalava
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35?
hartnn
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yup,35
Eyad
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Bingo!
lavalava
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what about
f(x)=x^2-4; g(x)=x+2
which is equal to (f+g)(x)
Eyad
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U mean Find F(F(x)+g(x)) ?
lavalava
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no its f(x)+g(x)
im not to sure but i think that might be it
hartnn
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then just add them
x^2-4+x+2 = ?
lavalava
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x^2+x-2?
hartnn
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yup
lavalava
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okay so what is f(x)=4x-1
g(x)=5x^2
which is equal to (fºg)(x)?
hartnn
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for (fog)(x) , replace 'x' in f(x) by g(x) = 5x^2
lavalava
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so then :
4(5x^2)-1
hartnn
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yup, that will be 20x^2-1
lavalava
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and then what is
f(x)=4x-7
g(x)=x+3
what is the function of (gºf)(4)
lavalava
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is it 12?
hartnn
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to get (gof)(x)
replace 'x' in g(x) by f(x) and then put x=4
hartnn
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yup, its 12
lavalava
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what is f(x)=5x-10
what is the value of f^-1 (-3)
hartnn
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so got that, its 1.4
lavalava
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yea
hartnn
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any more questions to come ?
lavalava
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yea
lavalava
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what is the vertex of the graph of f(x)=-2|x-5|+3
lavalava
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i think its -5, 3
Eyad
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+5,3
hartnn
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nopes, (5,3)
vertex for f(x) = p|x+a|+b
is -a,b
lavalava
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ohhh okay
lavalava
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the graph of g(x) results when the graph of f(x)=-|x| is shifted 3 units to the left.
i think it's g(x)=-|x+3|
lavalava
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what is the value of f(-4)
when f(x)=
-10 if x< -5
x^3 if -5≤x≤2
2x+4 if x>2
hartnn
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in which range does -4 lie ?
lavalava
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the middle one and the last one
hartnn
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not the last one, x>2 means x cannot be -4
so only middle one.
put x= -4 in middle function, what do u get ?
lavalava
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-64
hartnn
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thats your answer :)
lavalava
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okay now this one is kinda confusing to me but i think i know the answer....
lavalava
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i think it is the third one, but im not too sure....
hartnn
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nopes, its 4th.
put these values, x=0,0.5,1,1.5,..., find g(x)
u will get it
lavalava
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ohhhh i get it!!! its soo confusing sometimes!
lavalava
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f(x)=2x+5
g(x)=3x^2
which is equal to (fºg)(x)?
i tried it and i got 3x^2+2x+5 but i think it's wrong....
hartnn
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put x= 3x^2 in f(x)
2(3x^2)+5 = ?
lavalava
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6x^2+5?
hartnn
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yup.
lavalava
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omg you make it easier to understand hahaha
hartnn
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more questions ? i need to go...
lavalava
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yea one last one
f(x)=2/x
g(x)=|x|-1
what is the domain of (fºg)(x)
hartnn
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fog (x) = ?
lavalava
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x|x=real numbers
x|x ≠0
x|x≠0, x≠1
x|x≠-1, x≠1
hartnn
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f(g(x)) = 2/(|x|-1)
ok?
for which values is denominator = 0 ??
lavalava
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no the ones i put up last were the options
hartnn
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i know.
denominator should not be 0
|x|-1 should not be 0
for x=1, |1|-1=1-1=0
for x=-1, |-1|-1=1-1=0
so x|x≠-1, x≠1
got it ?
lavalava
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ohh okay yea! thank you! you make it easier to understand ty very much
hartnn
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welcome :)