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Consider the function
f(x) =1/2 (2x +2-x)
which has the graph
(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.
Differentiate following functions. (a) f ( x ) = 2 x 5 cosh x (b) h (t ) = sinh t / t + 1 Solution (a) f ′ ( x ) = 10x 4 cosh x + 2x 5 sinh x (b) h′ (t ) = (t
If the distances from origin of the centres of 3 circles x 2 +y 2 +2alphaix= a 2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+
where does goes take place?
Q. Graphing Sets of Numbers? Ans. To graph a set of numbers on a number line means to plot, or locate, those positions on the line. The number that corresponds to a poin
In this section we will be searching how to utilize Laplace transforms to solve differential equations. There are various types of transforms out there into the world. Laplace tran
Explain Comparing Fractions with example? If fractions are not equivalent, how do you figure out which one is larger? Comparing fractions involves finding the least common
Question 1 Explain Peano's Axioms with suitable example Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b 2 +1. Find a) (f °g
1.)3 3/8 divided by 4 7/8 plus 3 2.)4 1/2 minus 3/4 divided by 2 3/8
cos(x)y''+sin(x)y=2cos^3(x)sin(x)-1
111111-11111=
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