The function is defined by . What is the value of when ?
For function-evaluation questions like this, immediately rewrite the function with the given input in parentheses (for example, ). Then apply the order of operations carefully: handle exponents first (remember that squaring a negative gives a positive), then multiply, and finally add or subtract. Writing each step clearly helps avoid sign errors and is usually faster and safer than trying to do everything mentally under time pressure.
Hints
Start by using the function rule
Rewrite with replaced by . What expression do you get for ?
Be careful with the exponent
When you see , remember that you are multiplying by itself. Is the result positive or negative?
Follow order of operations
After you square , what do you do next: multiply by or subtract ? Do the operations step by step.
Desmos Guide
Define the function in Desmos
Type g(x) = 3x^2 - 5 into Desmos so it understands the function .
Evaluate the function at
In a new line, type g(-2) and look at the numerical output that Desmos shows. That number is the value of when .
Step-by-step Explanation
Substitute into the function
The function is . To find , replace with :
Be sure to keep in parentheses when you square it.
Square the input
Now square :
Substitute this back into the expression:
Multiply before subtracting
Multiply and :
Now the expression becomes:
Subtract to get the final value
Finally, subtract from :
So, , which corresponds to choice C.