Question 106·Easy·Nonlinear Functions
The function is defined by
What is the value of ?
(Express the answer as an integer)
For function-evaluation questions, rewrite the function with the given input substituted in place of the variable, then simplify step by step using order of operations: handle parentheses or expressions inside a square root first, then take the root or exponent, and finally do any additions or subtractions outside. Work neatly so you don’t forget parts of the expression, especially terms that come after a radical or parentheses.
Hints
Use the function definition
Start by writing using the definition by substituting .
Follow order of operations
After substituting, first simplify the expression inside the square root before doing anything else.
Finish carefully
Once you know the value of the square root, remember there is still a subtraction outside the square root that you must perform.
Desmos Guide
Evaluate the expression directly
In Desmos, type sqrt(7+9) - 3 exactly as written (or define g(y) = sqrt(y+9) - 3 and then enter g(7)). The single numerical result that Desmos shows is the value of .
Step-by-step Explanation
Substitute 7 into the function
The function is defined as
To find , replace with 7:
Simplify inside the square root
Add the numbers inside the square root:
So now the expression becomes
Evaluate the square root and subtract
Find the square root of 16 and then subtract 3:
So the value of is 1.