AP EAMCET202317 May 2023Morning ShiftMathematicsFunctionsActual
If f ( x ) is the signum function, then in terms of f ( x ) , the constant function g ( x )=1, x R is
Options
- Ag(x)= cases 2-f(x), & x < 0 f(x), & x 0 cases
- Bg(x)= cases f(x)+f(-x), & x < 0 f(x) f(-x), & x 0 cases
- Cg(x)= cases 1+f(x), & x>0 1-f(x), & x 0 cases
- Dg(x)= array cc f(x)+2, & x 0 array .
Correct answer
D. g(x)= array cc f(x)+2, & x 0 array .
Step-by-step solution
g(x)=1, x R and f(x)= cases -1 & x 0 cases aligned & for x 0: g(x)=1 & g(x)=0+1 & g(x)=0+f(x) & g(x)=f(x) aligned f(x)=1 So, g(x) can be written as g(x)= cases 2+f(x), & x 0 cases