AMA1110: Supplement Exercises 2
What covered in this exercise question set:
1. Basic concepts of functions: domain,
2. Polynomial functions
3. Operations of functions: f+g,f−g,f g,f
gand their domains
4. Composite function
5. Inverse function
6. Trigonometric functions
7. Rational functions
8. Periodic functions; Even/odd functions
1. Find the domain of the following functions:
(a) F(x) = p(x−1)(x+2);
(b) f(x) = 2
√x2−3x−10 .
2. * Find all values of csuch that the domain of f(x) = x+3
x2+3cx+6is the set of all real numbers.
3. Let f(x) = 1
2x−5and g(x) = √x−1.
(a) Find f+g,f g and f
g, and describe their domains;
(b) Find f◦gand g◦f.
4. Find the inverse functions for the following:
(a) y= (x+1)2+2, x≥ −1;
(b) y=x5−7;
(c) * y=64x3−48x+12
x−1
x3,x>1.
5. (a) If fis a one-to-one function such that f(2) = 9, what is f−1(9)?
(b) Let f(x) = 3+x2+tan(πx/2), where −1<x<1. Find f−1(3)and f(f−1(5))?
6.
Express the improper rational function
x4+4x3+3x2−3
x2+3x+2
into the addition of a polynomial and a
proper rational function. Figure out the degrees for the numerator
x4+
4
x3+
3
x2−
3 and
denominator x2+3x+2.
7. Find the following values by calculator:
(a) sin 1 (b) sin 1◦(c) sin−11 (d) (sin 1)−1
Remark: Please note the differences of notations in (c) and (d).
8. Determine if the function f(x)is even or odd or nerither.
(a) f(x) = x+1
x(b) g(x) = |cos(x)|(c) h(x) = (3+x)2−(3−x)2
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