Question

Find the value of b in the function f(x) ax + b if f^-1(3)=2 and f^-1(-3) = 6, where f^-1(x) is the inverse of the function f(x).
b=

Answer 1

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:

$y = f(x) = ax + b$

To find the inverse:

$x = ay + b$

$ay = x - b$

$y = \frac{x - b}{a}$

$f^{-1}(x) = \frac{x - b}{a}$

At x = 3, the inverse is 2, hence:

$2 = \frac{3 - b}{a}$

$2a = 3 - b$

$a = \frac{3 - b}{2}$

At x = -3, the inverse is 6, hence:

$6 = \frac{-3 - b}{a}$

$6a = -3 - b$

$a = \frac{-3 - b}{6}$

Equaling:

$\frac{3 - b}{2} = \frac{-3 - b}{6}$

$6(3 - b) = 2(-3 - b)$

$18 - 6b = -6 - 2b$

$4b = 24$

$b = \frac{24}{4}$

$b = 6$

To learn more about inverse functions, you can take a look at brainly.com/question/8824268