Question

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

Answer 1

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:

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