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Maths-

General

Easy

Question

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

Strictly increasing
Strictly decreasing
Neither increasing nor decreasing
None of these

hint Hint:

We are given a function. We have to find if it's increasing or decreasing. A function is increasing when it's first order derivative is positive. A function is decreasing when it's first order derivative is negative. We will find the first order derivative of the given function to find the answer.

The correct answer is: Strictly increasing

The given function is f(x) = $tan to the power of negative 1 end exponent open parentheses x close parentheses$
We will take the first-order derivative of the function.
$table attributes columnalign left end attributes row cell f open parentheses x close parentheses equals tan to the power of negative 1 end exponent open parentheses x close parentheses end cell row cell f apostrophe open parentheses x close parentheses equals fraction numerator 1 over denominator 1 plus x squared end fraction end cell row blank end table$
The quantity x² is always positive.
And all other values are positive constants.
So, the total value of the first-order derivative is positive.
It means f'(x) > 0
It means the given function is strictly increasing.

For such questions, we should check the rules of increasing and decreasing function.

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