Question

If F(x) = (x - 4)/3, H(x) = 3x + 4, and J(x) = √(x + 6), find the value of H(F(J(19))).

Answer 1

To find the value of H(F(J(19))), substitute the given expression into each function and simplify step by step. The final value is 5.

Step-by-step explanation:

To find the value of H(F(J(19))), we need to substitute the given expression into each function and simplify the result step by step.

1. First, evaluate J(19) by substituting 19 into the function J(x) = √(x + 6). Hence, J(19) = √(19 + 6) = √(25) = 5.
2. Next, substitute J(19) = 5 into the function F(x) = (x - 4)/3. Thus, F(J(19)) = F(5) = (5 - 4)/3 = 1/3.
3. Finally, substitute F(J(19)) = 1/3 into the function H(x) = 3x + 4. Therefore, H(F(J(19))) = H(1/3) = 3(1/3) + 4 = 1 + 4 = 5.

Therefore, the value of H(F(J(19))) is 5.