and

**Let’s look at f(g(x))
first:**

Since BOTH *f*(*g*(*x*))
AND *g*(*f*(*x*)) would have to equal *x* for them
to be inverses of each other and *f*(*g*(*x*)) is not
equal to *x*, then we can stop
here and say without a doubt that **they are NOT inverses of each
other**.

and

**Let’s look at f(g(x))
first:**

**Next, let’s look at g(f(x)):**

*Plug in the "value" of

**Since f(g(x))
AND g(f(x)) BOTH came out to be x, this
proves that the two functions are inverses of each other.**

Since this *y* is a function, it
is the inverse of the original
function.

See how the graphs of

If you need a review on graphing the cubic functions, feel free to go to College Algebra

The domain of *f* is
the same as the range of which is .

The range of *f* is the same as
the domain of which is .

If you need a review on
finding the domain and range of a function, feel free to go to College
Algebra **Tutorial
30: Introduction to Functions**.

If you need a review on finding the
domain and range of a graph of a function, feel
free to go to College Algebra **Tutorial
32: Graphs of Functions, Part II**.

Normally when we take the square root of
both sides, there
are two answers .. the + or – of the square root. But,
because it is only defined for greater than or equal to 0,
then that means we can only use the positive square root.

If we had both + and – in front of the square root, then this would not be a function and hence there would not be an inverse. But, we do have a function here, so we can carry on ….

If we had both + and – in front of the square root, then this would not be a function and hence there would not be an inverse. But, we do have a function here, so we can carry on ….

Since this *y* is a function, it
is the inverse of the original
function.

See how the graphs of

If you need a review on graphing the quadratic and square root functions, feel free to go to College Algebra

The
domain of *f* is the same as the range of which is .

The range of *f* is the same as
the domain of which is .

If you need a review on
finding the domain and range of a function, feel free to go to College
Algebra **Tutorial
30: Introduction to Functions**.

If you need a review on finding the
domain and range of a graph of a function, feel
free to go to College Algebra **Tutorial
32: Graphs of Functions, Part II**.

Last revised on June 24, 2010 by Kim Seward.

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