Composition of Functions - Grade 11 - General Mathematics | MATH TEACHER GON | YouTubeToText
YouTube Transcript: Composition of Functions - Grade 11 - General Mathematics
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hi guys it's me teacher going in today's
video we will talk about the composite
function or composition of function
so we have here this notation
this is read as f
circle of G of X or
F composite G of X and that is equal to
this notation f g of X we're in in this
function since the variable F or the
function f comes first before G
G will be the input or the input function
function
with respect to the function f so
without further Ado let's do this topic
we are given two different functions f
of x is equal to 3x minus 5 and the
other is 3x at 3 of x g of x
is equal to x squared plus two and right
evaluate this one we have f
of G of 2 and the other is G of f of
negative one let's start with number one
in this case RF of G of 2 here
first we will try to evaluate f
f
of G
of X that is the same as that
okay now what will happen here is that
in this case guys
we will move this one since
since
your function f
comes first before G
we will plug in
this x square plus 2
to replace the variable X in
3x minus five so it goes like this three
copy three
then your X this x will be replaced by x square
square
times x square
plus 2
that is f
look at this one your gfx is inside the
parenthesis this will be the input
so we will replace the variable x 3
times x square
plus 2 minus 5. so what will happen
is that we will replace this variable X
by 2 and it will become 3
times
2 square
plus 2 minus 5. so what will happen is
that you need to simplify this to become 3
3
times 2 squares four
plus two then we have minus five simplify
simplify three
three
times four plus two which is equal to six
six
and then minus 5.
so this is three times six is eighteen
minus five therefore
your f
of G
of 2 is equal to 15 minus 18 minus 5
which is equal to 13. guys don't be
confused about these two different
notations if the variable F comes first
meaning your input is
the function G
if the function G comes first
your function f will be the input okay
let's continue
here number two we have G of f of
negative one
so it will become G
G off
off f
f
we will use this and this 3x minus 5
will be replaced or we will be using
this to substitute for the value
variable X and it will become like this
x squared that is x squared by copy this one
one
3x minus 5 Square
Square
X squaring
now after doing that remember that you
are asked to evaluate negative one
we will replace this x by negative one
it will become 3
3
times negative one
minus 5 square plus two
so simplify that into three times
negative 1 is negative three
three
minus five
then square plus 2. so simplify that
until your negative three minus five is
negative eight Square
Square
plus 2 and negative 8
squared is not negative 64. right the
answer is 60 4 and then plus 2. therefore
therefore
of f
of negative 1
is equal to 64 plus 1 and that is 66.
and this is the answer guys
so I hope guys learned something from
this video on how to
evaluate composite functions so if
you're new to my channel don't forget to
like And subscribe button hit the Bell
button for you to be updated starting
latest uploads again it's me to turgon
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