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Exercises-Functions-1 - x 3-x b f R → R f x = x | x | c...

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MA100, Fall 2010, PART 1: Precalculus Functions - Exercises-1 1) Which of the sketches a) to f) represent functions? For each sketch representing a function, state the function’s domain and range. 2) Find the domain of the functions: a) f ( x ) = 2 x 2 - 5 x 2 x + 5 b) f ( x ) = x 2 - 3 x + 2 x 2 - 4 c) f ( x ) = 1 + 2 x - 4 + 3 x + 2 x 2 - 5 x + 6 d) f ( x ) = x - 2 e) f ( x ) = x - 2 + 3 x + 2 x 2 - 5 x + 6 f) f ( x ) = r 2 - x 2 x - 3 g) f ( x ) = r 8 - 4 x 4 x + 2 + 1 x h) f ( x ) = 5 x 2 + 6 x + r 1 3 - x i) f ( x ) = 5 5 x 2 + 6 x j) f ( x ) = 3 r 1 3 - x + 3 x + 2 1
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3) Consider f : R R , f ( x ) = 3 x - 4 , x ( -∞ , 0] 2 , x (0 , 2) 3 - 2 x - 2 x 2 , x [2 , ) Find f (2) , f 1 5 , f - 1 5 , f 7 4 . 4) Determine the range of the following functions: a) f : R R , f ( x ) = 2 x + 1 b) f : [ - 1 , 5] R , f ( x ) = 2 x + 1 c) f : ( -∞ , 0] R , f ( x ) = 2 x + 1 d) f : {- 1 , 0 , 1 , 2 , 3 } → R , f ( x ) = 2 x + 1 e) f : [ - 1 , 1] ∪ { 2 , 4 } → R , f ( x ) = 2 x + 1 5) Decide which functions are odd, which are even and which are none: a) f : R
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Unformatted text preview: x 3-x b) f : R → R , f ( x ) = x · | x | c) f : R → R , f ( x ) = x x 2 + 1 d) f : Z → Z , f ( x ) = x · (-1) x e) f : R → R , f ( x ) = ( x, x ∈ Q-x, x ∈ R \ Q Answers to selected exercises: 1) b) It is a function; the domain is { a,b,c } and the range is { 2 } d) It is a function; the domain is { a,c } and the range is { 2 } f) It is not a function. 2) b) x ∈ (-∞ , ∞ ) \ ± 2 d) x ∈ [2 , ∞ ) g) x ∈ ±-1 2 , 2 ³ \ 0 i) x ∈ (-∞ , ∞ ) 4) b) [-1 , 11] d) {-1 , 1 , 3 , 5 , 7 } e) [-1 , 3] ∪ { 5 , 7 } 5) b) odd d) odd 2...
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