Question

Evaluate the given function.
f(x) = 2x²2 +3; find f(x + 2) - [f(x) + 2]

Answer 1

To evaluate the given function, we substitute x + 2 for x in the function f(x) = 2x² + 3. Then, we simplify f(x + 2) - [f(x) + 2] by substituting the expressions obtained earlier and simplifying.

Step-by-step explanation:

To evaluate the given function, we substitute x + 2 for x in the function f(x) = 2x² + 3. So, f(x + 2) = 2(x + 2)² + 3. To find f(x + 2) - [f(x) + 2], we simply substitute the expression of f(x + 2) and f(x) obtained earlier into the given expression and simplify.

Let's calculate:

1. Substituting x + 2 in the function, we have: f(x + 2) = 2(x + 2)² + 3
2. Substituting x in the function f(x), we have: f(x) = 2x² + 3
3. Substituting these expressions in the given expression, we have:

f(x + 2) - [f(x) + 2] = [2(x + 2)² + 3] - [2x² + 3 + 2]

To calculate further, we expand the expression (x + 2)² and combine like terms.

Carrying out the simplification, we get the final answer as: 4x² + 4x + 5

Learn more about Evaluating a function