Question

F(x) = x^2 + 5x + 8

a) 2x + h + 8
b) 2x + h + 5
c) 2x^2 + 2x + 2xh + h^2 + h + 16
d) h

Answer 1

The expression that accurately represents
`\(f(x + h)\)` for the given function
`\(f(x) = x^2 + 5x + 8\)` is option (c)
`\(2x^2 + 2x + 2xh + h^2 + h + 16\).`

Explanation:

To determine
`\(f(x + h)\),` we substitute
`\(x + h\) into \(f(x) = x^2 + 5x + 8\)`, replacing each
`\(x\)` with
`\(x + h\).` The expanded and simplified result is
`\(f(x + h) = 2x^2 + (2x + 2xh) + (h^2 + 5h + 8)\)`. The correct option (c) precisely represents this expression, encompassing the correct terms and coefficients.

Understanding the process of substituting variables and simplifying expressions is fundamental in evaluating functions with altered inputs.

In this scenario, option (c) accurately denotes the function
`\(f(x + h)\)` for the provided quadratic function
`\(f(x)\).`