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Mathematics Question on Increasing and Decreasing Functions

Given: 5f(x)4f(1x)=x2−45f (x) 4f(\frac 1x) = x^2 - 4 & y=9f(x)×x2y = 9f(x) × x^2 If y is strictly increasing, then find interval of xx.

A

(−∞,−15]∪(15,0)(-∞, -\frac {1}{\sqrt 5}]∪(\frac {1}{\sqrt 5},0)

B

(−15,0)∪(0,15)(-\frac {1}{\sqrt 5},0)∪(0,\frac {1}{\sqrt 5} )

C

(0,15)∪(15,∞)(0,\frac {1}{\sqrt 5})∪(\frac {1}{\sqrt 5} ,∞)

D

(−25,0)∪(25,∞)(-\sqrt {\frac 25},0)∪(\sqrt {\frac 25},∞)

Answer

(−25,0)∪(25,∞)(-\sqrt {\frac 25},0)∪(\sqrt {\frac 25},∞)

Explanation

Solution

The correct option is (D): (−25,0)∪(25,∞)(-\sqrt {\frac 25},0)∪(\sqrt {\frac 25},∞)