In mathematics, evaluating a function means substituting a specific value for the variable. In this lesson, we will evaluate the function f(x) = 2x squared minus x plus 3 at x equals 1. This means we replace every x in the function with the value 1.
To evaluate f of 1, we substitute 1 for every occurrence of x in the function. So f of x equals 2 x squared minus x plus 3 becomes f of 1 equals 2 times 1 squared minus 1 plus 3.
Now we simplify the expression following the order of operations, often remembered by PEMDAS or BODMAS. First, we evaluate the exponent: 1 squared is 1. Then we perform multiplication: 2 times 1 is 2. Finally, we proceed with addition and subtraction from left to right.
Now we perform the final arithmetic. Two minus one equals one, and one plus three equals four. Therefore, f of 1 equals 4. This is our final answer.
To verify our result, let's go through the calculation again. F of 1 equals 2 times 1 squared minus 1 plus 3, which simplifies to 2 times 1 minus 1 plus 3, and finally 2 minus 1 plus 3 equals 4. This confirms our answer. Let's also try evaluating the function at x equals 2. F of 2 equals 2 times 2 squared minus 2 plus 3, which is 2 times 4 minus 2 plus 3, and that simplifies to 8 minus 2 plus 3 equals 9.