Functions Question 391
Question: A function f is defined by $ f(x)=x+\frac{1}{x}. $ Consider the following.
(1) $ {{(f(x))}^{2}}=f(x^{2})+2 $ (2) $ {{(f(x))}^{3}}=f(x^{3})+3f(x) $ Which of the above is/are correct?
Options:
A) (1) only
B) (2) only
C) Both (1) and (2)
D) Neither (1) nor (2)
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ f(x^{2})+2=x^{2}+\frac{1}{x^{2}}+2 $ $ ={{( x+\frac{1}{x} )}^{2}}={{{f(x)}}^{2}} $ And $ f(x^{3})+3f(x) $ $ =x^{3}+\frac{1}{x^{3}}+3( x+\frac{1}{x} ) $ $ ={{( x+\frac{1}{x} )}^{3}}={{{f(x)}}^{3}} $ Thus, both 1 and 2 are correct.
BETA
