problem archive
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Let N be the set of natural numbers. Define a real valued function \( f: N \rightarrow N \) by \( f(x) = 2x + 1 \). Using this definition, complete th... -
Define the real valued function f: R → R by y = f(x) = x for each x ∈ R. Such a function is called the identity function. -
Define the function f: R → R by y = f(x) = c, x ∈ R where c is a constant and each x ∈ R. Here domain of f is R and its range is {c}. -
Define the function f: R → R by y = f(x) = x², x ∈ R. Complete the Table given below by using this definition. What is the domain and range of this fu... -
Draw the graph of the function f: R → R defined by f(x) = x^3, x ∈ R -
Define the real valued function f: R − {0} → R defined by f(x) = 1/x, x ∈ R − {0}. Complete the Table given below using this definition. What is the d... -
Let f(x) = x^2 and g(x) = 2x + 1 be two real functions. Find (f + g)(x), (f - g)(x), (fg)(x), (f/g)(x). -
Let f(x) = sqrt(x) and g(x) = x be two functions defined over the set of non-negative real numbers. Find (f + g)(x), (f - g)(x), (fg)(x) and (f/g)(x). -
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2,1), (5,1), (8,1), (11,1), (... -
Find the domain and range of the following real functions: (i) f(x) = -|x| (ii) f(x) = sqrt(9 - x^2). -
A function f is defined by f(x) = 2x - 5. Write down the values of (i) f(0), (ii) f(7), (iii) f(-3). -
The function 't' which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by t(C) = (9C/5) + 32. Find (i) t(0) (ii) t... -
Find the range of each of the following functions. (i) f(x) = 2 - 3x, x ∈ R, x > 0. (ii) f(x) = x^2 + 2, x is a real number. (iii) f(x) = x, x is a re... -
Let R be a relation from Q to Q defined by R = {(a,b); a,b ∈ Q and a−b ∈ Z}. Show that (i) (a,a) ∈ R for all a ∈ Q (ii) (a,b) ∈ R implies that (b,a) ∈... -
Let f = {(1,1), (2,3), (0,−1), (−1,−3)} be a linear function from Z into Z. Find f(x). -
Find the domain of the function f(x) = (x^2 + 3x + 5)/(x^2 − 5x + 4). -
The function f is defined by f(x) = 1−x, x < 0; 1, x = 0; x+1, x > 0. Draw the graph of f(x). -
The relation f is defined by f(x) = \begin{cases} x^2, & 0 \leq x \leq 3 \\ 3x, & 3 \leq x \leq 10 \end{cases} The relation g is defined by g(x) = \be... -
If f(x) = \frac{2}{x}, find \frac{f(1.1) - f(1)}{(1.1 - 1)}. -
Find the domain of the function f(x) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}.