Question

If f and g are continuous functions with f(3)=5 and lim x-->3 [2f(x)-g(x)]= 4, find g(3)

Answer 1

Since
`f` is continuous, you know that


`\displaystyle\lim_(x\to3)f(x)=f(3)=5`

So,


`\displaystyle\lim_(x\to3)(2f(x)-g(x))=2f(3)-\lim_(x\to3)g(x)=10-g(3)=4`

where the limit for
`g` also is equal to the value of
`g(3)` because
`g` is also continuous. This means
`g(3)=6`.