f and g are functions such that f(x) = \frac{12}{\sqrt{x}} and g(x) = 3(2x + 1) (a) Find g(5) (b) Find gf(9) (c) Find g^{-1}(6) - Edexcel - GCSE Maths - Question 20 - 2020 - Paper 1

First, we need to find f(9):

$f(9) = \frac{12}{\sqrt{9}} = \frac{12}{3} = 4$

Next, we substitute f(9) into g:

$gf(9) = g(4) = 3(2(4) + 1)$

Calculating this gives:

$g(4) = 3(8 + 1) = 3(9) = 27$

Therefore, gf(9) = 27.

To find g^{-1}(6), we need to solve the equation:

$g(x) = 6$

This is:

$3(2x + 1) = 6$

Dividing both sides by 3 gives:

$2x + 1 = 2$

Subtracting 1 from both sides yields:

$2x = 1$

Thus,

$x = \frac{1}{2}$

Therefore, g^{-1}(6) = \frac{1}{2}.