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:
[tex]\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}[/tex]Now, we evaluate the function at x= -2:
[tex]\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}[/tex]Finally, we have to compute f(-4) - f(-2), which is:
[tex]f(-4)-f(-2)=79-15=64[/tex]Hence the answer is 64.
