Answer:
[tex] a) \: g(2) = 21 \\ \\b) \: \: \: \: \: x = 5 \\ \\ c) \: g(1) - f(3) = 1 \\ \\ d) \: f(g(2)) = 64[/tex]
Step-by-step explanation:
[tex]f(x) = 3x + 1[/tex]
[tex]g(x) = 2 {(x + 1)}^{2} + 3 [/tex]
a)
[tex]g(x) = 2 {(x + 1)}^{2} + 3 \\ g(2) = 2(2 + 1) ^{2} + 3 \\ = 2 {(3)}^{2} + 3 \\ = 2(9) + 3 \\ = 18 + 3 \\ g(2) = 21[/tex]
b)
[tex]f(x) = 3x + 1 \\ 16 = 3x + 1 \\ 3x = 16 - 1 \\ 3x = 15 \\ \\ x = \frac{15}{3} \\ \\ x = 5[/tex]
c)
[tex]g(x) = 2 {(x + 1)}^{2} + 3 \\ g(1) = 2 {(1 + 1)}^{2} + 3 \\ = 2 {(2)}^{2} + 3 \\ = 2(4) + 3 \\ = 8 + 3 \\ = 11 \\ \\ \\ f(x) = 3x + 1 \\ f(3) = 3(3) + 1 \\ = 9 + 1 \\ = 10 \\ \\ \\ g(1) - f(3) = 11 - 10 = 1[/tex]
d)
[tex]g(2) = 21 \\ \\ f(g(2)) = 3(21) + 1 \\ = 63 + 1 \\ = 64[/tex]
I hope I helped you^_^
