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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.
integral from 0 to pi of dx/(a+b*cos(x)
Properties of Dot Product - proof Proof of: If v → • v → = 0 then v → = 0 → This is a pretty simple proof. Let us start with v → = (v1 , v2 ,.... , vn) a
WHAT TWO SIX DIDGIT NUMBERS CAN YOU ADD 984,357
If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans: p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (
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Determine the second derivative for following functions. Q (t ) = sec (5t ) Solution : Following is the first derivative. Q′ (t
Q. How many permutations can you make of the word STATISTICS? Solution: There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'
P OLYNOMIALS : It is not once nor twice but times without number that the same ideas make their appearance in the world. 1. Find the value for K for which
can u tell me a website for iit-jee questions?
Gm signal is better than am signal becuase
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