Given the following functions: \( f(x)=x^{2}+3 x-10 \) \( g(x)=x-2 \) Find each of the values below. Give exact answers. a. \( (f+g)(-4)=\square \) b. \( (f-g)(2)=\square \) c. \( (f \cdot g)(-3)=\square \) d. \( \left(\frac{f}{g}\right)(4)=\square \)

To find the values requested, we will compute \( (f+g)(x) \), \( (f-g)(x) \), \( (f \cdot g)(x) \), and \( \left(\frac{f}{g}\right)(x) \) for the specified inputs. 1. **Finding \( (f+g)(-4) \)**: \[ f(-4) = (-4)^{2} + 3(-4) - 10 = 16 - 12 - 10 = -6 \] \[ g(-4) = -4 - 2 = -6 \] \[ (f+g)(-4) = f(-4) + g(-4) = -6 + (-6) = -12 \] 2. **Finding \( (f-g)(2) \)**: \[ f(2) = 2^{2} + 3(2) - 10 = 4 + 6 - 10 = 0 \] \[ g(2) = 2 - 2 = 0 \] \[ (f-g)(2) = f(2) - g(2) = 0 - 0 = 0 \] 3. **Finding \( (f \cdot g)(-3) \)**: \[ f(-3) = (-3)^{2} + 3(-3) - 10 = 9 - 9 - 10 = -10 \] \[ g(-3) = -3 - 2 = -5 \] \[ (f \cdot g)(-3) = f(-3) \cdot g(-3) = (-10) \cdot (-5) = 50 \] 4. **Finding \( \left(\frac{f}{g}\right)(4) \)**: \[ f(4) = 4^{2} + 3(4) - 10 = 16 + 12 - 10 = 18 \] \[ g(4) = 4 - 2 = 2 \] \[ \left(\frac{f}{g}\right)(4) = \frac{f(4)}{g(4)} = \frac{18}{2} = 9 \] Now, we can summarize the results: a. \( (f+g)(-4) = -12 \) b. \( (f-g)(2) = 0 \) c. \( (f \cdot g)(-3) = 50 \) d. \( \left(\frac{f}{g}\right)(4) = 9 \)