Question 229·Easy·Nonlinear Functions
The function is defined by . What is the value of ?
For simple function notation questions like this, immediately rewrite the expression by substituting the given input for , then follow the order of operations: handle exponents first, then addition or subtraction, and finally apply any fractions. Keep track of parentheses carefully so you know whether numbers are inside or outside the denominator, and then match your simplified result to the closest answer choice.
Hints
Understand what g(2) means
Think about what you do with the in the formula when you want to find .
Substitute first, then simplify
After you replace with 2, focus on simplifying the denominator: what does equal?
Finish simplifying the fraction
Once you know , put that number in the denominator under 1 and see which answer choice matches that fraction.
Desmos Guide
Enter the function and evaluate at x = 2
In Desmos, type g(x)=1/(x^2+1) to define the function. On the next line, type g(2) (or directly 1/(2^2+1)) and look at the numerical output that Desmos gives. Then choose the answer option that matches this value as a fraction.
Step-by-step Explanation
Interpret the function notation
The function is defined as . The expression means: take the formula for and replace every with .
So, start by writing
Evaluate the expression
Now simplify the denominator.
First compute the exponent: .
Then add 1: , so the denominator is 5.
That gives
Looking at the answer choices, this matches choice D.