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Aditya Potter
Mathematics
3 July, 10:36
What is the inverse of the fuction f (x) = x+3
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Kolby Huang
3 July, 10:41
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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
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