inverse, converse, and contrapositive?

• Jan 27th 2011, 05:41 PM
Jeonsah
inverse, converse, and contrapositive?
Hey guys got a question:

I have $\displaystyle f(x) = x^2$ and $\displaystyle f(x) = 9$

The problem is asking for the converse, inverse and contrapositive statments of those 2 functions. I am not familiar with this, can someone guide me as to what these mean?
• Jan 28th 2011, 01:32 AM
DrSteve
As far as I know a function doesn't have an inverse, converse or contrapositive (well maybe an inverse, but I don't think that's the definition you mean). You generally find the inverse, converse and contrapositive of a conditional statement. Either tell us the statement, or give the definitions of these expressions for functions.
• Jan 28th 2011, 04:24 AM
Soroban
Hello, Jeonsah!

I agree with DrSteve . . .

Quote:

$\displaystyle \text{I have: }\:f(x) = x^2\,\text{and }\,f(x) = 9$

$\displaystyle \text{The problem is asking for the converse, inverse and contrapositive}$
$\displaystyle \text{statments of those 2 functions.}$ . . This makes no sense.

The converse, inverse and contrapositive are variations of an implication.

If the original statement were: .$\displaystyle \text{If }f(x) = x^2,\text{ then }f(x) = 9$

. . then we have:

. . . . $\displaystyle \begin{array}{ccccc} \text{Converse:} & \text{If }f(x) = 9,\text{ then }f(x) = x^2. \\ \\[-3mm] \text{Inverse:} & \text{If }f(x) \ne x^2,\text{ then }f(x) \ne 9. \\ \\[-3mm] \text{C'positive:} & \text{If }f(x) \ne 9,\text{ then }f(x) \ne x^2. \end{array}$