Determine the largest possible domain and inverse function, Mathematics

Assignment Help:

Consider the function

f(x) =1/2 (2x +2-x)

which has the graph

677_graph.png

(a) Explain why f has no inverse function. You should include an example to support your explanation.

(b) Determine the largest possible domain, which includes x = 1, for f(x) such that the inverse function f-1(x) does exist.

(c) Given your answers in (b) find the inverse function f-1(x). Clearly explain key steps and show all working.

(d) Sketch the graph of y = f(x) for the restricted domain in (b) and y = f-1(x) on the same set of axes. All points of intersection and axes-intercepts should be easily determined from your sketch or clearly labelled. Furthermore axes should be clearly labelled with appropriate scaling. It is suggested you use different colours for the two graphs and clearly label each graph.


Related Discussions:- Determine the largest possible domain and inverse function

What is the volume of the water required to fill the pool, A circular pool ...

A circular pool is filling along with water. Supposing the water level will be 4 ft deep and the diameter is 20 ft, what is the volume of the water required to fill the pool? (π =

Multiplication and division, you want to share 34 pencils among 6 friends ....

you want to share 34 pencils among 6 friends .How many would each friend get?

Fractions, what is 1/3 + 2/9 equal

what is 1/3 + 2/9 equal

Evaluate the measure of the larger angle, Two angles are complementary. The...

Two angles are complementary. The calculate of one angle is four times the measure of the other. Evaluate the measure of the larger angle. a. 36° b. 72° c. 144° d. 18°

Calculate the average, During 2008 the average number of beds required per ...

During 2008 the average number of beds required per day at St Hallam's hospital was 1800.  During the first 50 days of 2008 the average daily requirement for beds was 1830, with a

Find out the x-y coordinates of the points - tangents, Find out the x-y coo...

Find out the x-y coordinates of the points in which the following parametric equations will have horizontal or vertical tangents. x = t 3 - 3t        y = 3t 2 - 9 Solut

each player selects one of her two remaining chips , Consider the followin...

Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only once. To beg

Angels, angel 1 and angel 2 are what angels?

angel 1 and angel 2 are what angels?

Analyze the dynamic path - difference equation, One of the well-known class...

One of the well-known class of models that involve a simple difference equation are models of mean reversion. These models typically take the form yt+1 - yt = -a(yt - μ)where 0

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd