Suppose f : N N has the rule f(n) = n2 .
Is f an invertible function? If not, why not.
[Remember that N represents the positive integers.]
a. Yes
b. No, the function is not one-to-one (but is onto).
c. No, the function is not onto (but is one-to-one).
d. No, the function is neither one-to-one nor onto.
Solution
b. No, the function is not one-to-one (but is onto)..
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Suppose f (x) = log(x) (a) Find f(0.1), f(1) and f(10)Suppose f .pdf
1. Suppose f (x) = log(x)
(a) Find f(0.1), f(1) and f(10)
Suppose f (x) = log(x)
(a) Find f(0.1), f(1) and f(10). No need to show work here, just give the answers.
(b) On graph paper - sketch a graph of f with these three points and the vertical
asymptote clearly indicated.
(c) On the same set of axes, sketch a graph of the transformation of the log given by
f (x + 2) + 3 . Show on your graph where the three points from parts (a) and (b) are on the
transformed graph.
(d) What is the domain of f (x) ? _____________
What is the domain of f (x + 2) + 3 ? ________________
Solution
a) -1,0,1
d)(0,Infinity)
(-2,infinity) these kind of brackets indactes that the end value doesnot belong to the set