The functions f and g are such that f(x) = 5x + 3 g(x) = ax + b where a and b are constants - Edexcel - GCSE Maths - Question 22 - 2017 - Paper 2

Next, we need to find f^{-1}(33). We first determine f(x):

$f(x) = 5x + 3$

To find the inverse, we set f(x) = y and solve for x:

$y = 5x + 3$

Rearranging gives:

x = rac{y - 3}{5}

Thus, the inverse function is:

f^{-1}(y) = rac{y - 3}{5}

Now substituting y = 33 into the inverse function:

f^{-1}(33) = rac{33 - 3}{5} = rac{30}{5} = 6

Given that f^{-1}(33) = g(1), we substitute x = 1 into g(x):

$g(1) = a(1) + b = a + b$

We have:

$a + b = 6$

This is our second equation, which we refer to as Equation (2). Now we can solve the simultaneous equations (1) and (2):

1. $3a + b = 20$
2. $a + b = 6$

Subtracting Equation (2) from Equation (1):

$3a + b - (a + b) = 20 - 6$ $2a = 14$ $a = 7$

Substituting the value of a back into Equation (2):

$7 + b = 6$ $b = 6 - 7$ $b = -1$