Question

Let f(x) = 5x^2 - 2x -9calculate f(-4) - f(-2)

Answer 1

We are required to evaluate the given function at x=-4 and at x=-2.

Let's start by evaluating the function when x=-4:

`\begin{gathered} f(x)=5x^2-2x-9 \\ f(-4)=5(-4)^2-2(-4)-9 \\ f(-4)=5*16+8-9 \\ f(-4)=79 \end{gathered}`

Now, we evaluate the function at x= -2:

`\begin{gathered} f(x)=5x^2-2x-9 \\ f(-2)=5(-2)^2-2(-2)-9 \\ f(-2)=5*4+4-9 \\ f(-2)=15 \end{gathered}`

Finally, we have to compute f(-4) - f(-2), which is:

`f(-4)-f(-2)=79-15=64`

Hence the answer is 64.