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

Customary units of length, Eileen needs 9 feet of fabric to make a skirt. I...

Eileen needs 9 feet of fabric to make a skirt. If Eileen has 18 feet of fabric how many skirts can she make?

Given the hypotenuse of a right triangle, Given the hypotenuse of a right t...

Given the hypotenuse of a right triangle: Given that the hypotenuse of a right triangle is 18" and the length of one side is 11", what is the length of another side? a 2 +

Describe about parallel and perpendicular lines, Describe about Parallel an...

Describe about Parallel and Perpendicular Lines ? Parallel Lines : Parallel lines are coplanar lines (lines that lie in the same plane) that never intersect. The bl

Arden''s Theorem, Find the Regular Grammar for the following Regular Expres...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Substitute 6 for r in the formula a = r^2 and solve for a, Find the area of...

Find the area of a circle along with a radius of 6 inches. The formula for the area of a circle is A = πr 2 . Use 3.14 for π. Substitute  6 for r in the formula A = πr 2 and solve

Rational expressions, Now we have to look at rational expressions. A ration...

Now we have to look at rational expressions. A rational expression is a fraction wherein the numerator and/or the denominator are polynomials.  Here are some examples of rational e

Logarithm, The function A(t) = 5(0.7)^t was used to define the amount A in ...

The function A(t) = 5(0.7)^t was used to define the amount A in milliliters of a drug in the bloodstream t hours after the drug was ingested. Determine algebraically the time it wi

Algebra, Evaluate: 30 - 12÷3×2 =

Evaluate: 30 - 12÷3×2 =

Percent problems.., I have a graph, i need to determine the many hours per ...

I have a graph, i need to determine the many hours per day becky spends on math activity if she does it 25% of her day.

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