Question

2.

f(x) = 3x +1 g(x) = 2(x + 1)2 + 3
Determine
a) g(2)
b) x when f(x)=16
c) g(1)-f(3)
d) f(g(2))

Answer 1

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

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 = (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^_^