Answer
\[
(G \circ F)(0) = 0,\quad
(G \circ F)(1) = 2,\quad
(G \circ F)(2) = 4,\quad
(G \circ F)(3) = 1,\quad
(G \circ F)(4) = 3.
\]
Work Step by Step
We have two functions:
1. \(F(a) = 7a\).
2. \(G(a) = a \bmod 5\).
Then \((G \circ F)(x) = G\bigl(F(x)\bigr) = G\bigl(7x\bigr) = 7x \bmod 5.\)
Evaluating this for \(x=0,1,2,3,4\):
1. \((G \circ F)(0) = 7\cdot 0 \bmod 5 = 0.\)
2. \((G \circ F)(1) = 7\cdot 1 \bmod 5 = 7 \bmod 5 = 2.\)
3. \((G \circ F)(2) = 7\cdot 2 \bmod 5 = 14 \bmod 5 = 4.\)
4. \((G \circ F)(3) = 7\cdot 3 \bmod 5 = 21 \bmod 5 = 1.\)
5. \((G \circ F)(4) = 7\cdot 4 \bmod 5 = 28 \bmod 5 = 3.\)
