Saved Bookmarks
| 1. |
If function sgn(x2 – 9x + 20) = 1, then find the value of x.1. (4, 5) 2. (5, ∞)3. (-∞, 4) 4. None of these |
| Answer» Correct Answer - Option 3 : (-∞, 4) CONCEPT:The real function f: R → R defined by\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\left| x \right|}}{x},\;\;\;x \ne 0} \\ {0,\;\;\;\;x = 0} \end{array}} \right. = \left\{ {\begin{array}{*{20}{c}} {1,\;\;\;\;\;\;\;if\;\;x > 0} \\ {0,\;\;\;\;\;\;\;if\;\;x = 0\;} \\ { - 1,\;\;\;\;\;\;\;\;\;if\;x < 0} \end{array}} \right.\)is called the signum function. Domain of f = R, Range of f = {1, 0, – 1}CALCULATIONS:Given function is f (x) = sgn(x2 – 9x + 20) = 1As we know that signum function gives 1, only when x > 0.∴ x2 – 9x + 20 > 0⇒ (x – 4) (x – 5) > 0So, x ∈ (-∞, 4) ⋃ (5, ∞) | |