Using inverse functions, it is found that b = 6.
Inverse function:
- To find the inverse function, we exchange x and y in the original function, then isolate f.
In this problem, the function is:
[tex]y = f(x) = ax + b[/tex]
To find the inverse:
[tex]x = ay + b[/tex]
[tex]ay = x - b[/tex]
[tex]y = \frac{x - b}{a}[/tex]
[tex]f^{-1}(x) = \frac{x - b}{a}[/tex]
At x = 3, the inverse is 2, hence:
[tex]2 = \frac{3 - b}{a}[/tex]
[tex]2a = 3 - b[/tex]
[tex]a = \frac{3 - b}{2}[/tex]
At x = -3, the inverse is 6, hence:
[tex]6 = \frac{-3 - b}{a}[/tex]
[tex]6a = -3 - b[/tex]
[tex]a = \frac{-3 - b}{6}[/tex]
Equaling:
[tex]\frac{3 - b}{2} = \frac{-3 - b}{6}[/tex]
[tex]6(3 - b) = 2(-3 - b)[/tex]
[tex]18 - 6b = -6 - 2b[/tex]
[tex]4b = 24[/tex]
[tex]b = \frac{24}{4}[/tex]
[tex]b = 6[/tex]
To learn more about inverse functions, you can take a look at https://brainly.com/question/8824268
