Question

If f(x) = x^2 + x - 2, find 4f(-a).

Options:
Option 1: 4(-a^2 - a - 2)
Option 2: -4a^2 - 4a - 8
Option 3: -4a^2 - 4a + 8
Option 4: 4a^2 + 4a - 8

Answer 1

The correct answer is 4a^2 - 4a - 8, obtained by substituting -a into the function f(x) = x^2 + x - 2 and then multiplying the result by 4.

Step-by-step explanation:

To find 4f(-a) when f(x) = x^2 + x - 2, we first substitute -a for x in the function:

f(-a) = (-a)^2 + (-a) - 2

This simplifies to:

f(-a) = a^2 - a - 2

Then, we multiply the entire function by 4:

4f(-a) = 4(a^2 - a - 2)

Which gives us:

4f(-a) = 4a^2 - 4a - 8

Therefore, the correct answer is Option 4: 4a^2 + 4a - 8.