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Let f(x)=x-(1)/(x) then which one of the...

Let `f(x)=x-(1)/(x)` then which one of the following statements is true?

A

f(x) is one-one function.

B

f(x) is increasing function.

C

f(x) = k has two distinct real roots for any real k.

D

x = 0 is point inflection.

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`f(x)=x-(1)/(x)`
`f'(x)=1+(1)/(x^(2))gt0`
`rArr" f is increasing"`
`f(1)=f(-1)=0`
`rArr" f(x) is many - one"`
`{:("When "xrarr0^(+)",",f rarr-oo),("When "xrarroo",",f rarroo),("When "x rarr0^(-)",",f rarr +oo),("and when "x rarr-oo",",f rarr-oo):}`
So the graph of the function is as shown in the figure.

From the graph any line y = k meets the curve at two distinct point.
Also `f''(x)=-2//x^(3)`
and `f''(x)lt0 " for "x gt0`
Hence x = 0 point of infection.
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