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If f(x)=1/(1-x) and g(x)=f[f{f(x)}] then g(x) is discontinuous at

 
If f(x)=1/(1-x) and g(x)=f[f{f(x)}] then g(x) is discontinuous at

Grade:12

4 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
g(x)=f[f{f(x)}]

=f[f{1/(1-x)}]
=f[1/{1-(1/(1-x)}]
=f[(x-1)/x]
=1/1-{(x-1)/x}
=1/[(x-x+1)/x]
=x
g(x)=x, which is a straight line passing through origin with slope 1.
so g(x) is continuous everywhere.

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

Shivam
39 Points
9 years ago
 
But sir answer is given x=0 and there is no options for everywhere continuous
RINKOO GUPTA
8 Points
9 years ago
you can  check th continuity of the function at x=0 
lhl at x-0 = lim h->0 f(0-h)
=lim h->0 (-h)
=0
RHL at x=0 =lim h->0 f(0+h)
=lim h->0 f(h)=lim h->0 ( h)=0
lhl=rhl 
so it is continous at x=0 
Roushan Mishra
26 Points
one year ago
g(x) is to be continuous if f(x) is continuous and f(x) is discountinuous at x=1 likewise when you'll solve f(f(x)) it will be discountinuous at x=0 

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