What is the inverse of the fuction f (x) = x+3

Inverse of function f (x) is y = x-3

Step-by-step explanation:

Given:

f (x) = (x+3)

To Find:

Inverse of f (x)

Solution:

Inverse of the function:

Let f: X - > Y be a function with domain X and target set Y. Then g is the inverse of f if g is a function with domain Y and target set X such that

g (f (x)) = x for all x in X

f (g (y)) = y for all y in Y.

f has an inverse function if and only if f is both one-to-one and onto. If f is one-to-one and onto, then its inverse function g is defined implicitly by the relation g (f (x)) = x.

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

Let y = f (x) = x+3

So, swapping the variables: y=x+3 becomes x=y+3

Now, solve the equation x=y+3 for y.

y=x-3

y=x-3