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

Nemeric patterns, Kelli calls her grandmother every month. Every other mont...

Kelli calls her grandmother every month. Every other month,Kelli also calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by the end

Probablity, probability as that of flipping a coin eight times and getting ...

probability as that of flipping a coin eight times and getting all the times the same side of the coin.)

What is exponents values, What is Exponents values? Exponents were inve...

What is Exponents values? Exponents were invented as a quick way to show that you are multiplying a number by itself several times. It's too much trouble to write something

Objectives of why learn mathematics, Objectives After studying this uni...

Objectives After studying this unit, you should be able to explain how mathematics is useful in our daily lives; explain the way mathematical concepts grow; iden

Velocity of a particle, A particle moves along a straight line so that afte...

A particle moves along a straight line so that after t secs its distance from fixed point O on the line is given by s=(t-1)^2(t-2).find the distance from O when the velocity is zer

Dot product - vector, Dot Product- Vector The other topic for discu...

Dot Product- Vector The other topic for discussion is that of the dot product.  Let us jump right into the definition of dot product. There is given that the two vectors a

Algebra, Manuel is a cross-country runner for his school’s team. He jogged ...

Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is 3 tim

Rotational symmetry .., write down the order of rotational symmetry of the ...

write down the order of rotational symmetry of the rectangle

I need help, in 2000,nearly 18% of cars in north America were sliver. what ...

in 2000,nearly 18% of cars in north America were sliver. what percent of the cars sold were not sliver?

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