| (1) \[{{(f(x))}^{2}}=f({{x}^{2}})+2\] |
| (2) \[{{(f(x))}^{3}}=f({{x}^{3}})+3f(x)\] |
| Which of the above is/are correct? |
A) (1) only
B) (2) only
C) Both (1) and (2)
D) Neither (1) nor (2)
Correct Answer: C
Solution :
[c] \[f({{x}^{2}})+2={{x}^{2}}+\frac{1}{{{x}^{2}}}+2\] \[={{\left( x+\frac{1}{x} \right)}^{2}}={{\{f(x)\}}^{2}}\] And \[f({{x}^{3}})+3f(x)\] \[={{x}^{3}}+\frac{1}{{{x}^{3}}}+3\left( x+\frac{1}{x} \right)\] \[={{\left( x+\frac{1}{x} \right)}^{3}}={{\{f(x)\}}^{3}}\] Thus, both 1 and 2 are correct.
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