माना कि `f : R to R ` में f(x) = x से परिभाषित है तथा `g : R to R` में `g(x) = |x|` से परिभाषित है तो निकालें
`(i) f +g" "(ii) f-g " "(iii) f*g " "(iv) alpha f, alpha in R" "(v) f/g`

Explanation

`f + g*f - g, f, g , alpha` functions from R to defined by
(i) `(f+g)(x) = f(x) + g (x) = x + |x|= {{:(0" ,"x le 0),(2x" ,"xge 0):}`
(ii)`(f-g)(x) = f (x) - g (x) = x - |x| = {{:(2x","x le 0),(0"," xge 0):}`
(iii)` (f*g)(x) = f(x) * g(x) = x |x| = {{:(-x^(2)","xle0),(x^(2)"," x"," ge 0):}`
(iv)` (alpha.f)(x) = alpha.f (x) = alpha x`
(v) ` f/g : R -{0} to R`में फलन है ।
`(f/g)(x)=(f(x))/(g(x)) = x/|x|={{:(-1"," xlt 0),(1"," x gt 0):}`