Final answer:
To find f(-7) with the given function f(x), substitute -7 for x, simplify the expression, and calculate the result. The value of f(-7) is -637.095.
Step-by-step explanation:
To find f(-7) of the function f(x) = -14 / (-20x + 7) - 13x^2, we substitute x = -7 into the function. This gives us:
f(-7) = -14 / (-20(-7) + 7) - 13(-7)^2
First, we simplify inside the parentheses:
= -14 / (140 + 7) - 13(49)
= -14 / 147 - 637
Next, we simplify the fraction and the multiplication:
= -14 / 147 - 637
Since -14/147 simplifies to -1/10.5 or approximately -0.095, and -637 is kept as is:
= -0.095 - 637
Finally, we add the two terms to find f(-7):
= -0.095 - 637
= -637.095