Question

Help would be appreciated!

Answer 1

First we need to determine the inverse of
$g(x) = 6x - 3$
Let
$y = g(x)$
This implies that,

$y = 6x - 3$
Now interchange x and y

$x = 6y - 3$
Make y the subject
$x + 3 = 6y$
$y = \frac{x + 3}{6}$
Now
$g {}^{ - 1} (x) = \frac{x + 3}{6}$
So
$g {}^{ - 1} (9) = \frac{9 + 3}{6}$
$g {}^{ - 1} (9) = \frac{12}{6}$
$g {}^{ - 1} (9) = 2$

$The correct answer is B.$

Answer 2

g(x) =  6x - 3

we find the inverse of g(x) by making x the subject of the equation:-

6x = g(x) + 3

x = (g(x) + 3) / 6

Replacing x by g-1(x) and g(x) by x:-

g-1(x) =  (x + 3)/ 6

So g-1(9)  = (9 + 3) / 6 =  2   answer