Question 55·Easy·Nonlinear Functions
The function is defined by
What is the value of ?
For function evaluation questions, immediately write the function with the given input substituted in place of , then simplify in a clear order: first simplify inside parentheses or in the denominator, then perform any division or multiplication, and finally handle addition or subtraction. Avoid mental shortcuts that skip steps; writing the intermediate expression (like ) helps prevent common mistakes such as ignoring a final + or − term or misreading the denominator.
Hints
Use the definition of the function
You are given . To find , think about what you should do with the in this formula.
Focus on the expression in the denominator
After you substitute , look carefully at the denominator . What does simplify to?
Work step by step
Once you have simplified , evaluate the fraction, and only then add the at the end. Keep the order of operations clear: parentheses/denominator first, then division, then addition.
Desmos Guide
Enter the function
In Desmos, type f(x) = 6/(x-1) + 2 so the calculator defines the function exactly as in the problem.
Create a table or plug in
Next to the function, click the gear icon and select "Table" (or type f(3) in a new line). In the table, enter in the -column, and look at the corresponding value; or, if you typed f(3), note the numerical output that Desmos shows.
Step-by-step Explanation
Substitute into the function
The function is defined as
To find , replace every in the formula with :
Simplify the denominator
First simplify the expression in the denominator:
So now the expression becomes
Evaluate the fraction
Now divide by :
So we have
Add to get the final value
Finally, add and :
Therefore, , which corresponds to answer choice C.