Question 148·Easy·Nonlinear Functions
The function is defined by . What is the value of ?
For function-evaluation questions, immediately replace the variable with the given input, keeping all parentheses and operations exactly as written. Simplify step by step—first the inside of any parentheses or radicals, then exponents or roots—before doing anything else. Be careful with square roots: means the positive number whose square is , not or , so always look for the single positive value.
Hints
Use the function rule
The function is given by . To find , think about what you should do with the in this expression.
Simplify inside the radical first
After you substitute , focus on simplifying the expression inside the square root before taking the square root itself.
Think about square roots
Once you have a number inside the square root, ask: "What positive number squared gives this value?" That positive number is the square root.
Desmos Guide
Evaluate the expression directly
In Desmos, type sqrt(7+9) into the expression line. Pay attention to the value Desmos shows for this expression; that is the value of .
Step-by-step Explanation
Substitute 7 into the function
The function is defined as . To find , replace with :
Simplify inside the square root
Add the numbers inside the square root before doing anything else:
So now you have
Evaluate the square root
The square root of 16 is the positive number whose square is 16:
So the value of is , which corresponds to choice B.