To evaluate the function f(x) = 2x² + 3x + 5 for the input value of 3, we need to substitute 3 into the function in place of x.
First, we replace x with 3:
f(3) = 2(3)² + 3(3) + 5
Now, let’s calculate each term:
- (3)² = 9, so 2(3)² = 2 * 9 = 18
- 3(3) = 9
- And we have the constant 5.
Adding these results together:
f(3) = 18 + 9 + 5 = 32
So, the value of the function f at x = 3 is 32.