Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
The value of the derivative of the function g(x) at x = 1 will be 1/3. Then the correct option is A.
What is an inverse function?
A function that may convert into another function is known as an inverse function or anti-function.
If the function is f(x) = sinx + 2x + 1.
Then the derivative of an inverse function g(x) of a function f(x) at a given value (a) will be
[tex]\rm g'(a) = \dfrac{1}{f'(g(a))}[/tex]
The derivative of f(x) will be
f'(x) = cos x + 2
Then the given value of a will be
a = 1
g(x) = f⁻¹(x)
put x = 0, then we have
f(0) = sin 0 + 2(0) + 1
f(0) = 1
Put x = 1, in the function f⁻¹(x). Then we have
f⁻¹(1) = 0
and
g(1) = 0
Then put a = 1, then we have
[tex]\rm g'(a) = \dfrac{1}{f'(g(a))}\\\\g'(1) = \dfrac{1}{f'(g(1))}\\\\g'(1) = \dfrac{1}{f'(0)}\\\\g'(1) = \dfrac{1}{\cos 0 + 2}\\\\g'(1) = \dfrac{1}{1+2}= \dfrac{1}{3}[/tex]
More about the inverse function link is given below.
https://brainly.com/question/2541698
#SPJ4
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
