f is a continous function in `[a, b]`; g is a continuous function in [b,c]. A function h(x) is defined as `h(x)=f(x) for x in [a,b) , g(x) for x in (b,c]` if f(b) =g(b) then

Options

A. `h(b^(+))=g(b^(-))` and `h(b^(-))=f(b^(+))`
B. `h^(b^(-))=g(b^(+))` and `h(b^(+))=f(b^(-))`
C. `h(x)` can be made continuous at `x=b` by by defining it at the point `x=b`
D. `f(a)=g(c)`

Answer

B, C

Explanation

`h(x)` is continous in `[a,b)cup(b,c]`
`becauseh(b^(-))=f(b^(+))` are undefined
`h(b^(-))=f(b^(-))=f(b)=g(b)=g(b^(+))`
and `h(b^(+))=g(b^(+))=g(b)=f(b)=f(b^(-))`
Hence `h(b^(-))=h(b^(+))=f(b)=g(b)`
Thus, `h(x)` has removable discontinuity at `x=b`