Answer:
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:
<em><u> Inverse of the function:</u></em>
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
