21.G. Let f be a function on R to R? which is differentiable on a neighborhood of a point c and such that Df (c) has an inverse. Then is it true that f has an inverse on a neighborhood of c?
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
please help with exercise 21.G
detailed solution for you to understand
![21.G. Let f be a function on R to R? which is differentiable on a neighborhood
of a point c and such that Df (c) has an inverse. Then is it true that f has an
inverse on a neighborhood of c?
21.H. Let f be a funetion on Rº to RP. If f is differentiable at c and has a
differentiable inverse, then is it true that Df(c) is one-one?
21.1. Suppose that f is differentiable on a neighborhood of a point c and that
if e > 0 then there exists 6(e) > 0 such that if |r - c| < ô(e), then |Df(x) (2) –
Df(c) (2) < elz| for all z in RP. Prove that the partial derivatives of f exist and
are continuous at c.
21.J. Suppose that Lo is a one-one linear function on Rr to R. Show that
there exists a positive number a such that if L is a linear function on Rr to R
satisfying](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecfdf914-0bc6-4db1-8ff8-1cb1dcbe37e9%2F2e165914-36da-42a1-bf0a-807fd5bbb9d9%2Ft3vzxh_processed.png&w=3840&q=75)
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