Question

2.

Answer 1

Answer:

$a) \: g(2) = 21 \\ \\b) \: \: \: \: \: x = 5 \\ \\ c) \: g(1) - f(3) = 1 \\ \\ d) \: f(g(2)) = 64$

Step-by-step explanation:

$f(x) = 3x + 1$

$g(x) = 2 {(x + 1)}^{2} + 3$

a)

$g(x) = 2 {(x + 1)}^{2} + 3 \\ g(2) = 2(2 + 1) ^{2} + 3 \\ = 2 {(3)}^{2} + 3 \\ = 2(9) + 3 \\ = 18 + 3 \\ g(2) = 21$

b)

$f(x) = 3x + 1 \\ 16 = 3x + 1 \\ 3x = 16 - 1 \\ 3x = 15 \\ \\ x = \frac{15}{3} \\ \\ x = 5$

c)

$g(x) = 2 {(x + 1)}^{2} + 3 \\ g(1) = 2 {(1 + 1)}^{2} + 3 \\ = 2 {(2)}^{2} + 3 \\ = 2(4) + 3 \\ = 8 + 3 \\ = 11 \\ \\ \\ f(x) = 3x + 1 \\ f(3) = 3(3) + 1 \\ = 9 + 1 \\ = 10 \\ \\ \\ g(1) - f(3) = 11 - 10 = 1$

d)

$g(2) = 21 \\ \\ f(g(2)) = 3(21) + 1 \\ = 63 + 1 \\ = 64$

I hope I helped you^_^