A function that is bounded above has an infinite number of

Chapter 1, Problem 1.168

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A function that is bounded above has an infinite number of upper bounds, but there is always a least upper bound, i.e., an upper bound that is less than all the others. This least upper bound may or may not be in the range of f. For each of the following functions, find the least upper bound and tell whether or not it is in the range of the function.

(a) \(f(x)=2-0.8 x^{2}\)

(b) \(g(x)=\frac{3 x^{2}}{3+x^{2}}\)

(c) \(h(x)=\frac{1-x}{x^{2}}\)

(d) \(p(x)=2 \sin (x)\)

(e) \(q(x)=\frac{4 x}{x^{2}+2 x+1}\)

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