Respuesta :
The inverse of f(X) = (x +6 ) /5
What is inverse function?
The inverse of a function f is denoted by f^-1 and it exists only when f is both one-one and onto function. Note that f^-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x.
(f o f^-1) (x) = (f^-1 o f) (x) = x
Steps To Find An Inverse Function
The following sequence of steps would help in conveniently finding the inverse of a function. Here we consider a function f(x) = ax + b, and aim at finding the inverse of this function through the following steps.
- For the given function f(x) = ax + b, replace f(x) = y, to obtain y = ax + b.
- Interchange the x with y and the y with x in the function y = ax + b to obtain x = ay + b.
- Here solve the expression x = ay + b for y. And we obtain y = (x - b/a
- Finally replace y = f^-1(x), and we have f^-1(x) = (x - b)/a.
Given:
f(x) = 5x – 6
let y= f(x) = 5x – 6
Now, Interchange the x with y and the y with x.
x= 5y -6
x+6 = 5y
y = (x +6 ) /5
So, f^-1(x) = (x +6 ) /5
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