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

Given f and g are continuous functions.

∴ `lim_(x -> 3) f(x) = f(3)`  ........(1)

`lim_(x -> 3) g(x) = g(3)`   ........(2)

Given `f(3)` = 5 and

`lim_(x -> 3) [2f(x) - g(x)]` = 4

`lim_(x -> 3) 2f(x) - lim_(x -> 3) g(x)` = 4

`2 lim_(x -> 3) f(x) - lim_(x -> 3) g(x)` = 4

2f(3) – g(3) = 4

2 × 5 – g(3) = 4

10 – 4 = g(3)

g(3) = 6