Question 157·Easy·Nonlinear Functions
The function is defined by . What is the value of ?
For function-evaluation questions like this, treat the input (here, 1) as a substitution: replace every in the function with that number, simplify step by step (inside parentheses or square roots first), and only then apply any outer operations like square roots or exponents. Staying organized—writing on each line as you simplify—helps avoid stopping too early or making small arithmetic mistakes.
Hints
Use the function rule
Focus on the definition . What should you do to in this rule to find ?
Work inside the square root first
After you replace with , carefully simplify the expression . What number do you get inside the square root?
Handle the square root last
Once you know the number inside the square root, think: what non-negative number squared gives that result?
Desmos Guide
Evaluate the expression directly
In Desmos, type sqrt(9*1+16) exactly as written (including the sqrt and parentheses). The numerical output that Desmos shows is the value of ; match that value to the correct answer choice.
Step-by-step Explanation
Interpret the function notation
The expression means: take the function rule for and replace every with .
So start from
and write
Simplify inside the square root
Now simplify the expression under the square root sign.
Compute the value inside:
So we have
Evaluate the square root and choose the matching option
The symbol means the principal (non-negative) square root. The number whose square is 25 and is non-negative is 5, because .
So
This corresponds to answer choice B) 5.