Question 223·Easy·Nonlinear Functions
The function is defined by . What is the value of ?
For function-evaluation questions, always start by carefully substituting the given input into the function rule, keeping all operations (like +5) exactly as written. Then simplify the inside of any parentheses or square roots first, and finally perform the outer operation. Check whether the final number is a familiar perfect square to avoid unnecessary approximations and quickly match it to one of the answer choices.
Hints
Use the function rule
The function is defined by . To find , what should you do with in the formula?
Simplify step by step
After substituting , simplify the expression under the square root sign before taking the square root.
Think about perfect squares
Once you simplify inside the square root, ask yourself: is that number a perfect square? What whole number squared gives that value?
Desmos Guide
Evaluate the function value directly
In a Desmos expression line, type sqrt(11+5) and press Enter. The value that appears to the right is the value of from the function .
Step-by-step Explanation
Substitute 11 into the function
The function is defined as
To find , replace with :
Simplify inside the square root
Now add the numbers inside the square root:
so
Evaluate the square root and match the answer choice
The square root of is because .
So
Looking at the choices, this corresponds to C) 4.