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Example Questions
Example Question #31 : Algebra Of Functions
Let
Determine .
To find the composite function we start from the most inner portion of the expression and work our way out.
Example Question #32 : Algebra Of Functions
Let
Determine
.
The composite funtion means to replace every entry x in f(x) with the entire function g(x).
Example Question #11 : Composition Of Functions
For ,
, and
, determine
.
Working inside out, first do .
This is,
.
Now we will do .
This is
Example Question #14 : Composition Of Functions
For , write a function for
.
Working from the inside out, first we will find a function for .
This is:
, which we can simplify slightly to
.
Now we will plug this new function into the function k:
.
Since ln is the inverse of e to any power, this simplifies to .
Example Question #13 : Composition Of Functions
Find given the following equations
To find simply substiute
for every x in
and solve.
Example Question #16 : Composition Of Functions
If and
, find
.
First, make sure that g
f (range of g is a subset of the domain of f).
Since the g:
and
f:
,
g
f and
exists.
Plug in the output of , which is
, as the input of
.
Thus,
Example Question #17 : Composition Of Functions
Find and evaluate at
.
"G of F of X" means substitute f(x) for the variable in g(x).
Foil the squared term and simplify:
First:
Outer:
Inner:
Last:
So
Now evaluate the composite function at the indicated value of x:
Example Question #14 : Composition Of Functions
Find if
and
.
Replace and substitute the value of
into
so that we are finding
.
Example Question #15 : Composition Of Functions
Given and
, find
.
Given and
, find
.
Begin by breaking this into steps. I will begin by computing the step, because that will make the late steps much more manageable.
Next, take our answer to and plug it into
.
So we are close to our final answer, but we still need to multiply by 3.
Making our answer 84.
Example Question #16 : Composition Of Functions
Given and
, find
.
None of the other answers.
and is read as "g of f of x" and is equivalent to plugging the function f(x) into the variables in the function g(x).
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