Given the following functions, find each of the values: \( f(x)=x^{2}-4 \) \( g(x)=x-2 \) \( (f+g)(5)= \) \( (f-g)(-3)=\square \) \( (f \cdot g)(2)=\square \) \( \left(\frac{f}{g}\right)(-4)=\square \)

Let's calculate each of the required values step by step. 1. **Finding \((f+g)(5)\)**: \[ f(5) = 5^2 - 4 = 25 - 4 = 21 \] \[ g(5) = 5 - 2 = 3 \] \[ (f+g)(5) = f(5) + g(5) = 21 + 3 = 24 \] 2. **Finding \((f-g)(-3)\)**: \[ f(-3) = (-3)^2 - 4 = 9 - 4 = 5 \] \[ g(-3) = -3 - 2 = -5 \] \[ (f-g)(-3) = f(-3) - g(-3) = 5 - (-5) = 5 + 5 = 10 \] So, \((f-g)(-3) = 10\). 3. **Finding \((f \cdot g)(2)\)**: \[ f(2) = 2^2 - 4 = 4 - 4 = 0 \] \[ g(2) = 2 - 2 = 0 \] \[ (f \cdot g)(2) = f(2) \cdot g(2) = 0 \cdot 0 = 0 \] So, \((f \cdot g)(2) = 0\). 4. **Finding \(\left(\frac{f}{g}\right)(-4)\)**: \[ f(-4) = (-4)^2 - 4 = 16 - 4 = 12 \] \[ g(-4) = -4 - 2 = -6 \] \[ \left(\frac{f}{g}\right)(-4) = \frac{f(-4)}{g(-4)} = \frac{12}{-6} = -2 \] In summary, we have: \((f+g)(5) = 24\), \((f-g)(-3) = 10\), \((f \cdot g)(2) = 0\), and \(\left(\frac{f}{g}\right)(-4) = -2\).