Let `f(x)=x^(3)+x` be function and
`g(x)={(f(|x|)",", x ge 0),(f(-|x|)",",x lt 0):}`, then

Options

A. g(x) is continuous `AA x in R`
B. g(x) is continuous, `AA x in R^(-)` only
C. g(x) is continuous, `AA x in R^(+)` only
D. g(x) is discontinuous, `AA x in R^(-)`

Answer

A

Explanation

`g(x) ={(x^(3)+x"," ,x ge 0),(x^(3)+x"," ,x lt 0):}`
`[because f(|x|)=f(x)" for " x ge 0 and f(-|x|)=f[-(-x)]=f(x) " for " x lt 0]`
`rArr g(x)=x^(3)+x, AA x in R`
Hence, continuous for all ` x in R` .