00:01
Upon the question.
00:01
So, function is given to us and we need to find out f inverse dash of 1.
00:06
So, we can write that f of f dash or f inverse is always equal to identity and similarly this is also equal to f inverse of n.
00:15
So, from here we can say that f inverse of fx will be equal to i of x for all x.
00:24
Next we can say that f inverse that is f inverse for f of x will be equal to i of x.
00:35
We can also write this as i of x.
00:38
So, this will be equal to x.
00:40
So, let us say this is equation number 1.
00:43
So, from equation number 1 we can say that differentiating with chain rule.
00:53
So, when we differentiate with chain rule we will get f inverse dash of f of x multiplied by f dash x will be equal to 1 because differentiation of x will be equal to 1.
01:09
So, from here we can say that f inverse whole inverse of f of x will be equal to 1 divided by f dash x.
01:17
Let us say this is equation number 2.
01:21
Next we have f of x is equal to 1 suppose.
01:26
So, suppose f of x is equal to 1.
01:29
So, from equation 2 we can say or from the equation above equation of 2x plus e to the power 5x we can write it implies that 2x plus e to the power 5x will be equal to 1 which is 5x...