A) No solution
B) Exactly one solution
C) At most one solution
D) Atleast three solutions
Correct Answer: D
Solution :
(d)If \[f\left( a \right)=a,\]then obviously \[x=a\]is the solution |
Let \[f\left( a \right)>a\]and \[g\left( x \right)=f\left( x \right)-x\]then \[g\left( a \right)>0\]and \[g\left( f\left( a \right) \right)=f\left( f\left( a \right) \right)-f\left( a \right)=a-f\left( a \right)<0\] |
Since\[~g\left( x \right)~\]is continuous, so at least for one \[c\in \left( a,f\left( a \right) \right),g\left( c \right)=0.\] |
Similarly we can argue for\[f\left( a \right)<a\] |
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