Given that \( f(x)=(x-4)^{2} \) and \( g(x)=1-5 x \), find (a) \( (f+g)(-4)=\square \) (b) \( (f-g)(-4)=\square \) (c) \( (f g)(-4)=\square \) (d) \( \left(\frac{f}{g}\right)(-4)=\square \)

To solve the given expressions, we first need to evaluate \( f(-4) \) and \( g(-4) \). 1. Calculate \( f(-4) \): \[ f(-4) = (-4 - 4)^2 = (-8)^2 = 64 \] 2. Calculate \( g(-4) \): \[ g(-4) = 1 - 5(-4) = 1 + 20 = 21 \] Now we can find the required expressions: (a) \( (f+g)(-4) \): \[ (f+g)(-4) = f(-4) + g(-4) = 64 + 21 = 85 \] (b) \( (f-g)(-4) \): \[ (f-g)(-4) = f(-4) - g(-4) = 64 - 21 = 43 \] (c) \( (fg)(-4) \): \[ (fg)(-4) = f(-4) \cdot g(-4) = 64 \cdot 21 = 1344 \] (d) \( \left(\frac{f}{g}\right)(-4) \): \[ \left(\frac{f}{g}\right)(-4) = \frac{f(-4)}{g(-4)} = \frac{64}{21} \] Now we compile the results: (a) \( (f+g)(-4) = 85 \) (b) \( (f-g)(-4) = 43 \) (c) \( (fg)(-4) = 1344 \) (d) \( \left(\frac{f}{g}\right)(-4) = \frac{64}{21} \)