anonymous
  • anonymous
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)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
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=.....
anonymous
  • anonymous
35?
hartnn
  • hartnn
yup,35

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anonymous
  • anonymous
Bingo!
anonymous
  • anonymous
what about f(x)=x^2-4; g(x)=x+2 which is equal to (f+g)(x)
anonymous
  • anonymous
U mean Find F(F(x)+g(x)) ?
anonymous
  • anonymous
no its f(x)+g(x) im not to sure but i think that might be it
hartnn
  • hartnn
then just add them x^2-4+x+2 = ?
anonymous
  • anonymous
x^2+x-2?
hartnn
  • hartnn
yup
anonymous
  • anonymous
okay so what is f(x)=4x-1 g(x)=5x^2 which is equal to (fºg)(x)?
hartnn
  • hartnn
for (fog)(x) , replace 'x' in f(x) by g(x) = 5x^2
anonymous
  • anonymous
so then : 4(5x^2)-1
hartnn
  • hartnn
yup, that will be 20x^2-1
anonymous
  • anonymous
and then what is f(x)=4x-7 g(x)=x+3 what is the function of (gºf)(4)
anonymous
  • anonymous
is it 12?
hartnn
  • hartnn
to get (gof)(x) replace 'x' in g(x) by f(x) and then put x=4
hartnn
  • hartnn
yup, its 12
anonymous
  • anonymous
what is f(x)=5x-10 what is the value of f^-1 (-3)
hartnn
  • hartnn
so got that, its 1.4
anonymous
  • anonymous
yea
hartnn
  • hartnn
any more questions to come ?
anonymous
  • anonymous
yea
anonymous
  • anonymous
what is the vertex of the graph of f(x)=-2|x-5|+3
anonymous
  • anonymous
i think its -5, 3
anonymous
  • anonymous
+5,3
hartnn
  • hartnn
nopes, (5,3) vertex for f(x) = p|x+a|+b is -a,b
anonymous
  • anonymous
ohhh okay
anonymous
  • anonymous
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|
anonymous
  • anonymous
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
  • hartnn
in which range does -4 lie ?
anonymous
  • anonymous
the middle one and the last one
hartnn
  • hartnn
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 ?
anonymous
  • anonymous
-64
hartnn
  • hartnn
thats your answer :)
anonymous
  • anonymous
okay now this one is kinda confusing to me but i think i know the answer....
anonymous
  • anonymous
i think it is the third one, but im not too sure....
hartnn
  • hartnn
nopes, its 4th. put these values, x=0,0.5,1,1.5,..., find g(x) u will get it
anonymous
  • anonymous
ohhhh i get it!!! its soo confusing sometimes!
anonymous
  • anonymous
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
  • hartnn
put x= 3x^2 in f(x) 2(3x^2)+5 = ?
anonymous
  • anonymous
6x^2+5?
hartnn
  • hartnn
yup.
anonymous
  • anonymous
omg you make it easier to understand hahaha
hartnn
  • hartnn
more questions ? i need to go...
anonymous
  • anonymous
yea one last one f(x)=2/x g(x)=|x|-1 what is the domain of (fºg)(x)
hartnn
  • hartnn
fog (x) = ?
anonymous
  • anonymous
x|x=real numbers x|x ≠0 x|x≠0, x≠1 x|x≠-1, x≠1
hartnn
  • hartnn
f(g(x)) = 2/(|x|-1) ok? for which values is denominator = 0 ??
anonymous
  • anonymous
no the ones i put up last were the options
hartnn
  • hartnn
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 ?
anonymous
  • anonymous
ohh okay yea! thank you! you make it easier to understand ty very much
hartnn
  • hartnn
welcome :)

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