Question

19 fand g are functions such that

12
(c)
and g(x)=3(2x + 1)
(a) Find g(5)
(b) Find gf(9)

Answer 1

(a) 33

(b) 27

(c) 1/2

Explanation:

(a)

g(x) = 3(2x + 1)

g(5) = 3(2 * 5 + 1)

g(5) = 3(10 + 1)

g(5) = 3(11)

g(5) = 33

(b)

`f(x) = (12)/(√(x))`

`f(9) = (12)/(√(9))`

`f(9) = (12)/(3)`

`f(9) = 4`

g(f(9)) = g(4) = 3(2(4) + 1)

g(f(9)) = 3(9)

g(f(9)) = 27

(c)

`g(x) = 3(2x + 1)`

`y = 3(2x + 1)`

`x = 3(2y + 1)`

`2y + 1 = (x)/(3)`

`2y = (x)/(3) - 1`

`y = (x)/(6) - (1)/(2)`

`g^(-1)(x) = (x)/(6) - (1)/(2)`

`g^(-1)(6) = (6)/(6) - (1)/(2)`

`g^(-1)(6) = 1 - (1)/(2)`

`g^(-1)(6) = (1)/(2)`

Answer 2

=3(2(5)+1

=3×10+1

=30+1

=31