Let f (x) = x2 − 2x. Determine a domain on which f−1 exists, and find a formula for f−1 for this domain of f .

Q: Show that f(x) = √æ³ + 1 is a one-to-one function. Then find its inverse.

A: We have given function fx=x3+15 fx1=x13+15 fx2=x23+15 Put fx1=fx2 x13+15=x23+15 x13+1=x23+1 x13=x23…

Q: Consider the function f(x) =V3x+6 for the domain[-2, 00). Find f(x), where fis the inverse of f. 1…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.