Given that \( f(x)=(x-6)^{2} \) and \( g(x)=5-3 x \), find (a) \( (f+g)(-1)=\square \) (b) \( (f-g)(-1)=\square \) (c) \( (f g)(-1)=\square \) (d) \( \left(\frac{f}{g}\right)(-1)=\square \) Question Help: Video Submit Question

Let's evaluate each part step by step using the given functions: \[ f(x) = (x - 6)^2 \] \[ g(x) = 5 - 3x \] We need to find the values of \( f(-1) \) and \( g(-1) \) first. ### Step 1: Calculate \( f(-1) \) and \( g(-1) \) \[ f(-1) = (-1 - 6)^2 = (-7)^2 = 49 \] \[ g(-1) = 5 - 3(-1) = 5 + 3 = 8 \] --- ### (a) \( (f + g)(-1) \) \[ (f + g)(-1) = f(-1) + g(-1) = 49 + 8 = 57 \] **Answer:** \( 57 \) --- ### (b) \( (f - g)(-1) \) \[ (f - g)(-1) = f(-1) - g(-1) = 49 - 8 = 41 \] **Answer:** \( 41 \) --- ### (c) \( (f \cdot g)(-1) \) \[ (f \cdot g)(-1) = f(-1) \times g(-1) = 49 \times 8 = 392 \] **Answer:** \( 392 \) --- ### (d) \( \left(\frac{f}{g}\right)(-1) \) \[ \left(\frac{f}{g}\right)(-1) = \frac{f(-1)}{g(-1)} = \frac{49}{8} = 6.125 \] You can leave the answer as an improper fraction or a decimal, depending on the required format. **Answer:** \( \frac{49}{8} \) or \( 6.125 \) --- ### Summary of Answers - **(a)** \( 57 \) - **(b)** \( 41 \) - **(c)** \( 392 \) - **(d)** \( \frac{49}{8} \) or \( 6.125 \)