Chapter 1: Problem 30
In Exercises \(21-30\) , determine whether the function is even, odd, or neither. Try to answer without writing anything (except the answer). $$y=\frac{1}{x^{2}-1}$$
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In Exercises 49 and \(50,\) (a) draw the graph of the function. Then find its (b) domain and (c) range. $$f(x)=2|x+4|-3$$
One-to-One Functions If \(f\) is a one-to-one function, provethat \(g(x)=-f(x)\) is also one-to-one.
Even-Odd (a) Show that \(\csc x\) is an odd function of \(x\) . (b) Show that the reciprocal of an odd function is odd.
In Exercises \(63-66,\) (a) graph \(f \circ g\) and \(g \circ f\) and make a conjecture about the domain and range of each function. (b) Then confirm your conjectures by finding formulas for \(f \circ g\) and \(g \circ f\) . $$f(x)=\frac{2 x-1}{x+3}, g(x)=\frac{3 x+1}{2-x}$$
In Exercises \(39-42,\) draw the graph and determine the domain and range of the function. $$y=\log _{2}(x+1)$$
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