We are going to evaluate the function f of x equals 2 x squared minus x plus 3 at x equals 2. First, let's understand what function evaluation means. It's the process of substituting a specific value for the variable x in the function.
Now we substitute x equals 2 into our function. We replace every instance of x with 2. So f of x becomes f of 2, 2 x squared becomes 2 times 2 squared, minus x becomes minus 2, and plus 3 remains the same.
Now we apply the order of operations, often remembered by PEMDAS or BODMAS. First, we evaluate the exponent: 2 squared equals 4. Next, we perform multiplication: 2 times 4 equals 8. Our expression now becomes 8 minus 2 plus 3.
Finally, we perform the addition and subtraction from left to right. First, 8 minus 2 equals 6. Then, 6 plus 3 equals 9. Therefore, f of 2 equals 9. Let's box our final answer.
To reinforce our understanding, let's evaluate the function at another value. We'll try x equals negative 1. Substituting negative 1 for x gives us f of negative 1 equals 2 times negative 1 squared minus negative 1 plus 3. Evaluating the exponent, negative 1 squared equals 1. So we have 2 times 1 plus 1 plus 3. Multiplying gives us 2 plus 1 plus 3, which equals 6. Therefore, f of negative 1 equals 6.