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If f(x)=x and g(x)=|x|, then define the ...

If `f(x)=x and g(x)=|x|`, then define the following functions:
`(i) f+g " "(ii) f-g`
`(iii) f*g" "(iv) (f)/(g)`

Text Solution

Verified by Experts

The correct Answer is:
(i) (f + g) (x) = `{{:(2x"," , x ge 0) , (0 "," , x lt 0):}` `" "(ii) (f-g)(x)={{:(0",",x ge 0),(2x",",x lt 0):}`
`(iii) (f*g)(x)={{:(x^(2)",",x ge 0),(-x^(2)",",x lt 0):} " "(iv)((f)/(g))(x)={{:(0",",x ge 0),(-1",",x lt 0):}`
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