# Thread: inverse, converse, and contrapositive?

1. ## inverse, converse, and contrapositive?

Hey guys got a question:

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

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?

2. 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.

3. Hello, Jeonsah!

I agree with DrSteve . . .

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

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

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

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

. . then we have:

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