Question

19 fand g are functions such that

Answer 1

Answer:

=3(2(5)+1

=3×10+1

=30+1

=31

Answer 2

Answer:

(a) 33

(b) 27

(c) 1/2

Step-by-step 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)

$f(x) = \dfrac{12}{\sqrt{x}}$

$f(9) = \dfrac{12}{\sqrt{9}}$

$f(9) = \dfrac{12}{3}$

$f(9) = 4$

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

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

g(f(9)) = 27

(c)

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

$y = 3(2x + 1)$

$x = 3(2y + 1)$

$2y + 1 = \dfrac{x}{3}$

$2y = \dfrac{x}{3} - 1$

$y = \dfrac{x}{6} - \dfrac{1}{2}$

$g^{-1}(x) = \dfrac{x}{6} - \dfrac{1}{2}$

$g^{-1}(6) = \dfrac{6}{6} - \dfrac{1}{2}$

$g^{-1}(6) = 1 - \dfrac{1}{2}$

$g^{-1}(6) = \dfrac{1}{2}$