We are going to evaluate the function f of x equals 2 x squared minus x plus 3 at x equals 5. 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 5 into our function. We replace every instance of x with 5. So f of x becomes f of 5, and 2x squared minus x plus 3 becomes 2 times 5 squared minus 5 plus 3. Notice how we use parentheses around the 5 to maintain proper order of operations.
Now we apply the order of operations, often remembered by PEMDAS or BODMAS. First, we evaluate the exponent: 5 squared equals 25. Then we perform multiplication: 2 times 25 equals 50. This transforms our expression step by step from 2 times 5 squared minus 5 plus 3 to 2 times 25 minus 5 plus 3 to 50 minus 5 plus 3.
Finally, we complete the arithmetic from left to right. First, 50 minus 5 equals 45. Then, 45 plus 3 equals 48. Therefore, f of 5 equals 48. This means that when x equals 5, the function value is 48. We can box our final answer to emphasize the result.
Let's verify our solution by quickly going through the steps again. We start with f of x equals 2 x squared minus x plus 3. Substitute x equals 5 to get f of 5 equals 2 times 5 squared minus 5 plus 3. This becomes 2 times 25 minus 5 plus 3, which is 50 minus 5 plus 3, and finally equals 48. Our answer is confirmed. We can summarize this in a table showing input x equals 5 and output f of 5 equals 48. This point (5, 48) would lie on the graph of our function. This process of substitution and evaluation applies to any function at any given point.