Explanation:
For (f + g)(x):
1. Enter f(x) = 4x^(2/3) and g(x) = 16x^(4/3) into the graphing calculator.
2. Press the Y= button to view the equations.
3. Press the Math button, then scroll down to the "fnInt" command and press Enter.
4. In the parentheses, enter f(x) + g(x), with "dx" after the parentheses.
5. Press Enter. The calculator should graph the integral of f(x) + g(x).
6. Press the Trace button, then use the arrow keys to move the cursor to x = 5.
7. The y-value given is the value of (f + g)(x) when x = 5.
Using this method, we get (f + g)(5) ≈ 57.57.
For (f - g)(x):
1. Follow the same steps as above, but in step 4, enter f(x) - g(x) instead of f(x) + g(x).
2. Follow the remaining steps as before.
3. Using this method, we get (f - g)(5) ≈ -403.08.
For (4)(x)(x):
1. Enter y = 4x^2 into the Y= menu.
2. Press the Trace button, then enter x = 5 for the value of x.
3. The y-value given is the value of (4)(x)(x) when x = 5.
4. Using this method, we get (4)(5)(5) = 100.
For (fg)(x):
1. Enter f(x) = 5x^3 and g(x) = 20x^(1/4) into the graphing calculator.
2. Press the Y= button to view the equations.
3. Press the Math button, then scroll down to the "fnInt" command and press Enter.
4. In the parentheses, enter f(x)g(x), with "dx" after the parentheses.
5. Press Enter. The calculator should graph the integral of f(x)g(x).
6. Press the Trace button, then use the arrow keys to move the cursor to x = 5.
7. The y-value given is the value of (fg)(x) when x = 5.
8. Using this method, we get (fg)(5) ≈ 354.75.