A) positive integers
B) whole numbers
C) prime numbers
D) all integers
Correct Answer: B
Solution :
\[f(x)=[{{4}^{x}}-{{2}^{x+1}}+1],\] Let \[{{2}^{x}}=t\] \[[{{t}^{2}}-2t+1]\] \[=[{{(t-1)}^{2}}]=\,[{{({{2}^{x}}-1)}^{2}}]\] If \[x=0,\] then \[f(x)=0\] Otherwise, \[{{({{2}^{x}}-1)}^{2}}\] is always greater than zero, so range is \[x\,\,\in \,\,\{0,\,1,\,\,2,\,\,3,...\}\] i.e, the set of the whole numbers.
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