Precalculus : Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1304 : Pre Calculus

Find given the following equations

Possible Answers:

Correct answer:

Explanation:

To find simply substiute for every x in and solve.

Example Question #1305 : Pre Calculus

If and , find 

Possible Answers:

Correct answer:

Explanation:

First, make sure that gf (range of g is a subset of the domain of f).

Since the g:  and f: gf and  exists.

Plug in the output of , which is , as the input of .

Thus, 

Example Question #171 : Functions

Find  and evaluate at .

Possible Answers:

Correct answer:

Explanation:

"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 #172 : Functions

Find  if  and .

Possible Answers:

Correct answer:

Explanation:

Replace  and substitute the value of  into  so that we are finding .

Example Question #173 : Functions

Given  and , find .

Possible Answers:

Correct answer:

Explanation:

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 #174 : Functions

Given    and   , find .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

 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).

 

Example Question #177 : Functions

 and  .  Find   .

Possible Answers:

Correct answer:

Explanation:

 and  .  

To find  we plug in the function  everywhere there is a variable in the function .

This is the composition of "f of g of x". 

Foil the square and simplify:

Example Question #178 : Functions

If  and , what must  be?

Possible Answers:

Correct answer:

Explanation:

Evaluate the composite function  first.

Solve for  by substituting  into the  value for .

The value of  will be replaced inside , which will become .

Evaluate .

The value of  is .  Add one to this value.

The answer is .

Example Question #1311 : Pre Calculus

Find  given

and

 

Possible Answers:

Correct answer:

Explanation:

To evaluate, first evaluate  and then plug in that answer into . Thus,

Then,  is

Example Question #180 : Functions

Find  given the following.

Possible Answers:

Correct answer:

Explanation:

To solve, plug 1 into g and then your answer into f.

Thus,

Plugging in this value into our f function we get the final answer as follows.

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