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

probability: complying with this treatment, A national study found that tr...

A national study found that treating people appropriately for high blood pressure decreased their overall mortality rate by 20%. Treating people adequately for hypertension has bee

Prove asymptotic bounds for recursion relations, 1. (‡) Prove asymptotic b...

1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n

Give an equations with the variable on both sides, Give an Equations with t...

Give an Equations with the variable on both sides ? Many equations that you encounter will have variables on both sides. Some of these equations will even contain grouping sy

If she remains going at similar rate how long will it take, Susan traveled ...

Susan traveled 114 miles in 2 hours. If she remains going at the similar rate, how long will it take her to go the remaining 285 miles of her trip? There is a 1 in 6 chance of

Logarithms, find any integer from 1-128 on a logarithmic scale

find any integer from 1-128 on a logarithmic scale

Tables and funcuctions, write an equation for a functionthat gives the valu...

write an equation for a functionthat gives the value in ech table .

Important points about the alternating series test, Important Points About ...

Important Points About the Alternating Series Test There are a several things to note about this test.  Very first, unlike the Integral Test and the Comparison or Limit Compari

Polynomials, give an example of a binomial of degree 27?

give an example of a binomial of degree 27?

Diffrence between rational and irrational numbers, Q. Diffrence between Rat...

Q. Diffrence between Rational and Irrational Numbers? Ans. A number which is not rational is called irrational. The word "irrational" sounds not quite right...as though th

By the method of completion of squares solve equation, By the method of com...

By the method of completion of squares show that the equation 4x 2 +3x +5 = 0 has no real roots. Ans:    4 x 2 +3 x +5=0 ⇒  x 2 + 3/4 x + 5 = 0 ⇒   x 2 + 3/4 x +

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