# The real number x when added to its inverse gives the maximum value of the sum at x equal to?

##
A: 1

B: -1

C: 2

D: -2

THE ANSWER IS (A) FOR YOU REFERENCE

A: 1

B: -1

C: 2

D: -2

THE ANSWER IS (A) FOR YOU REFERENCE

##### 1 Answer

The answer may be C to maximise the value of

#### Explanation:

The word "inverse" in the question is ambiguous, since

If the question is asking about the additive inverse (opposite), then the sum is always

If the question is asking about the multiplicative inverse (reciprocal), then it is asking us to maximise:

#f(x) = x + 1/x#

If

**Possible interpretation 1**

Given that this is a multiple choice question, then one interpretation that makes some sense is that we want to choose the option that maximises the value of the function.

We find:

A:

#" "f(1) = 1+1/1 = 2# B:

#" "f(-1) = -1+1/(-1) = -2# C:

#" "f(2) = 2+1/2 = 5/2# D:

#" "f(-2) = -2+1/(-2) = -5/2#

So the option that maximises

**Possible interpretation 2**

The function

Here's a graph...

graph{(y-x-1/x)((x+1)^2+(y+2)^2-0.01) = 0 [-10, 10, -5, 5]}

Note that *minimum* at

**Possible interpretation 3**

The question might actually be asking for the value of the sum at the maximum rather than the value of

#f(-1) = -2#