Given that \( f(x)=x^{2}-13 x \) and \( g(x)=x+9 \), find (a) \( (f+g)(-5)=\square \) (b) \( (f-g)(-5)=\square \) (c) \( (f g)(-5)=\square \) (d) \( \left(\frac{f}{g}\right)(-5)=\square \) Question Help: Video Submit Question

To solve the given problems, let's first evaluate the functions \( f(x) \) and \( g(x) \) at \( x = -5 \). 1. **Calculate \( f(-5) \)**: \[ f(-5) = (-5)^{2} - 13(-5) = 25 + 65 = 90. \] 2. **Calculate \( g(-5) \)**: \[ g(-5) = -5 + 9 = 4. \] Now we can solve each part: (a) **Calculate \( (f + g)(-5) \)**: \[ (f + g)(-5) = f(-5) + g(-5) = 90 + 4 = 94. \] So, \( (f + g)(-5) = 94 \). (b) **Calculate \( (f - g)(-5) \)**: \[ (f - g)(-5) = f(-5) - g(-5) = 90 - 4 = 86. \] So, \( (f - g)(-5) = 86 \). (c) **Calculate \( (fg)(-5) \)**: \[ (fg)(-5) = f(-5) \cdot g(-5) = 90 \cdot 4 = 360. \] So, \( (fg)(-5) = 360 \). (d) **Calculate \( \left(\frac{f}{g}\right)(-5) \)**: \[ \left(\frac{f}{g}\right)(-5) = \frac{f(-5)}{g(-5)} = \frac{90}{4} = 22.5. \] So, \( \left(\frac{f}{g}\right)(-5) = 22.5 \). To summarize: (a) \( (f+g)(-5) = 94 \) (b) \( (f-g)(-5) = 86 \) (c) \( (fg)(-5) = 360 \) (d) \( \left(\frac{f}{g}\right)(-5) = 22.5 \)