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If a function f : X → Y defined as f(x) = y is one-one and onto, then we can define a unique function g : Y → X such that g(y) = x, where x ∈ X and y = f(x), y ∈ Y. Function g is called the inverse of function f. The domain of sine function is R and function sine : R → R is neither one-one nor onto. The following graph shows the sine function. Let sine function be defined from set A to [– 1, 1] such that inverse of sine function exists, i.e., sin⁻¹ x is defined from [– 1, 1] to A. On the basis of the above information, answer the following questions :
If f : [3, ∞) → B given by f(x) = x² − 6x + 14 is a bijection, then B is equal to
Let f(x) = x2 and g(x) = 2x + 1 be two real functions. Find (f + g) (x), (f –g) (x), (fg) (x), (f/g)(x).
Let f(x) = √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).
Find the domain and range of the following real functions:
Find the range of each of the following functions.
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