Precalculus : Algebra of Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #11 : Add, Subtract, Multiply, And Divide Functions

Add the following functions:

Possible Answers:

Correct answer:

Explanation:

To add, simply combine like terms. Thus, the answer is:

Example Question #12 : Add, Subtract, Multiply, And Divide Functions

Given the functions:   and , what is ?

Possible Answers:

Correct answer:

Explanation:

For , substitute the value of  inside the function for  and evaluate.

For , substitute the value of  inside the function for  and evaluate.

Subtract .

The answer is:  

Example Question #13 : Add, Subtract, Multiply, And Divide Functions

Simplify  given,

 

Possible Answers:

Correct answer:

Explanation:

To solve , simply multiply your two functions. Thus,

Example Question #21 : Add, Subtract, Multiply, And Divide Functions

If and , find .

Possible Answers:

Correct answer:

Explanation:

To solve this problem, you must plug in the g function to wherever you see x in the f function. When you plug that in, it looks like this: . Then simplify so that your answer is: .

Example Question #22 : Add, Subtract, Multiply, And Divide Functions

Find given    and  .

Possible Answers:

The answer is not present.

Correct answer:

Explanation:

The problem is asking to find the composite function that results when f(x) is divided by g(x).

When dividing fractions, it is important to remember to multiply by the inverse.

Cross cancel the exponents leaving only one "x" in the bottom.

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 #3 : 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 #1 : 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,

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