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Example Questions
Example Question #51 : Pre Calculus
What is the domain of the following function?

The denominator becomes zero whenever cos(x) becomes 1 and this happens when x is an odd multiple of . To avoid division by zero, we exclude all these numbers. Therefore the domain is:
Example Question #1 : Evaluate Functions
Given and , evaluate .
We are given two functions and asked to find f(h(7)).
I would begin by finding h(7)
Now that we know h(7), we go ahead and plug it into f(x).
So our final answer is simply 8.
Example Question #2 : Evaluate Functions
Solve the function.
Determine the domain of .
Multiply on both sides of the equation to cancel the denominator and divide the equation by ten.
Since the domain states that , the only possible answer is .
Example Question #3 : Evaluate Functions
Solve for :
Rewrite so that the exponential variable is isolated.
Reconvert to a similar base. Use exponents to redefine the terms.
Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.
Solve for .
Example Question #4 : Evaluate Functions
Evaluate the following function when
Evaluate the following function when
To evaluate this function, simply plugin 6 for t and simplify:
So our answer is:
Example Question #5 : Evaluate Functions
Determine the value of of the function
In order to determine the value of of the function we set The value becomes
As such
Example Question #6 : Evaluate Functions
Find the difference quotient of the function .
Difference quotient equation is
and
.
Now plug in the appropriate terms into the equation and simplify:
Example Question #7 : Evaluate Functions
Find the value of the following function when
The function is undefined at
The function is undefined at
Find the value of the following function when
To evaluate this function, plug in 2 for x everywhere it arises and simplify:
So our answer must be undefined, because we cannot divide by
Example Question #8 : Evaluate Functions
Find the value of when
Find the value of when
To evaluate this expression, plug in the given value of everywhere you see a and simplify:
So our answer is:
Example Question #9 : Evaluate Functions
If , what is ?
In order to evaluate this function, simply substitute the value of as a replacement of .
Simplify using the order of operations.
The answer is:
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