Given: \(5f (x) 4f(\frac 1x) = x^2 - 4 \) & \(y = 9f(x) × x^2\) If y is strictly increasing, then find interval of \(x\).
\((-∞, -\frac {1}{\sqrt 5}]∪(\frac {1}{\sqrt 5},0)\)
\((-\frac {1}{\sqrt 5},0)∪(0,\frac {1}{\sqrt 5} )\)
\((0,\frac {1}{\sqrt 5})∪(\frac {1}{\sqrt 5} ,∞)\)
\((-\sqrt {\frac 25},0)∪(\sqrt {\frac 25},∞)\)
The Correct Option is D
Solution and Explanation
The correct option is (D): \((-\sqrt {\frac 25},0)∪(\sqrt {\frac 25},∞)\)
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Concepts Used:
Increasing and Decreasing Functions
Increasing Function:
On an interval I, a function f(x) is said to be increasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) ≤ f(y)
Decreasing Function:
On an interval I, a function f(x) is said to be decreasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) ≥ f(y)
Strictly Increasing Function:
On an interval I, a function f(x) is said to be strictly increasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) < f(y)
Strictly Decreasing Function:
On an interval I, a function f(x) is said to be strictly decreasing, if for any two numbers x and y in I such that x < y,
⇒ f(x) > f(y)
Graphical Representation of Increasing and Decreasing Functions
