Precalculus : Composition of Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 : Composition Of Functions

Suppose and 

What would  be?

Possible Answers:

Correct answer:

Explanation:

Substitute  into the function  for .

Then it will become:

Example Question #2 : Composition Of Functions

What is ?

Possible Answers:

Correct answer:

Explanation:

f(g(x)) simply means: where ever you see an x in the equation f(x), replace it with g(x).

So, doing just that, we get 

,

which simplifies to 

.

Since 

 our simplified expression becomes,

.

Example Question #2 : Composition Of Functions

What is ?

Possible Answers:

Correct answer:

Explanation:

g(f(x)) simply means replacing every x in g(x) with f(x).

After simplifying, it becomes

Example Question #4 : Composition Of Functions

For the functions

and

.

Evaluate the composite function

.

Possible Answers:

DNE

Correct answer:

Explanation:

The composite function means to plug in the function of  into the function  for every x value in the function.

Therefore the composition function becomes:

.

Example Question #5 : Composition Of Functions

For the functions

and

.

Evaluate the composite function

.

Possible Answers:

DNE

Correct answer:

Explanation:

The composite function means to plug in the function  into  for every x value.

Therefore the composite function becomes,

Example Question #5 : Composition Of Functions

If , and , what is ?

Possible Answers:

Correct answer:

Explanation:

When doing a composition of functions such as this one, you must always remember to start with the innermost parentheses and work backward towards the outside.

So, to begin, we have

 .

Now we move outward, getting 

.

Finally, we move outward one more time, getting 

.

Example Question #7 : Composition Of Functions

Find  if  , and .

Possible Answers:

Correct answer:

Explanation:

Solve for the value of .

Solve for the value of .

Solve for the value .

Example Question #6 : Composition Of Functions

For the functions  and , evaluate the composite function  

Possible Answers:

Correct answer:

Explanation:

The composite function notation  means to swap the function  into  for every value of . Therefore:

Example Question #161 : Functions

For the functions  and , evaluate the composite function 

Possible Answers:

Correct answer:

Explanation:

The composite function notation  means to swap the function  into  for every value of . Therefore:

Example Question #10 : Composition Of Functions

For the functions  and , evaluate the composite function .

Possible Answers:

None of the answers listed

Correct answer:

Explanation:

The composite function notation  means to swap the function  into  for every value of . Therefore:

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