If $f (x) = x + 3$ $f(x)=x+3$ how do you find the inverse?

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Answer 1 · 2016-11-25T18:59:37

Please see the explanation.

Given: Find the inverse of $f (x) = x + 3$ $f(x) = x + 3$

Substitute $f^{- 1} (x)$ $f^-1(x)$ for every x:

$f (f^{- 1} (x)) = f^{- 1} (x) + 3$ $f(f^-1(x)) = f^-1(x) + 3$

By definition, $f (f^{- 1} (x)) = x$ $f(f^-1(x)) = x$ :

$x = f^{- 1} (x) + 3$ $x = f^-1(x) + 3$

Solve for $f^{- 1} (x)$ $f^-1(x)$

$f^{- 1} (x) = x - 3$ $f^-1(x) = x - 3$

Check by verifying that f(f^-1(x)) = f^-1(f(x)) = x:

$f (f^{- 1} (x)) = (x - 3) + 3 = x$ $f(f^-1(x)) = (x - 3) + 3 = x$

$f^{- 1} (f (x)) = (x + 3) - 3 = x$ $f^-1(f(x)) = (x + 3) - 3 = x$

This checks.

If f(x)=x+3f(x)=x+3f(x)=x+3 how do you find the inverse?