If the function sgn (x² – 9x + 20) = 1, then what will be the value of x.

Question

Question

Answer 1

CONCEPT:

The real function f: R → R defined by

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) = 1

As we know that signum function gives 1, only when x > 0.

∴ x² – 9x + 20 > 0

⇒ (x – 4) (x – 5) > 0

So, x ∈ (-∞, 4) ⋃ (5, ∞)