Answer
$
a-\\
F(4, 4) = (9,10) \\
b-\\
F(2, 1) = (5,1) \\
c-\\
F(3, 2) = (7,4) \\
d-\\
F(1, 5) = (3,13) \\
$
Work Step by Step
$F: \mathbb{Z} \times \mathbb{Z}\rightarrow \mathbb{Z} \times \mathbb{Z}\\
\,For\,all\,ordered\,pairs\,(a, b)\,of\,\,integers \\
F(a, b) = (2a + 1, 3b-2) \\
a-\\
F(4, 4) = (2(4) + 1, 3(4)-2)=(9,10) \\
b-\\
F(2, 1) = (2(2) + 1, 3(1)-2)=(5,1) \\
c-\\
F(3, 2) = (2(3) + 1, 3(2)-2)=(7,4) \\
d-\\
F(1, 5) = (2(1) + 1, 3(5)-2)=(3,13) \\
$
