Question

The range of f(x) = sgn (x2) is


{1}


{0}


{–1}


{0, 1}

Answer 1

Given : f(x) = sgn (x²)

To find :  Range of f(x)

Solution:

f(x) = sgn (x²)

The sign of a real number, also called sgn or signum, is -1 for a negative numbers (i.e., one with a minus sign "), 0 for the number zero, or +1 for a positive numbers (i.e., one with a plus sign").

Lets check  three cases

x < 0   , x  = 0   & x  > 0

f(x) = sgn (x²)

x < 0  => x ² > 0

=> sgn (x²)   = 1

x = 0  => x ² =  0

=>  sgn (x²)   = 0

x > 0  => x ² > 0

=>  sgn (x²)   = 1

{0, 1}   is the Rage of   f(x) = sgn (x²)

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