If f(x) and g(x) are continuous functions with f(6)= 3 and limit as x approaches 0 of (5f(x) - g(x)) = 4, what is g(6)?
5 f(0) - g(0) = 4
g(0) = 5 f(0)-4
perhaps g(6) = 5 f(6) - 4 = 11
but that assumes a linear relationship between g and f, not just continuous, namely
g(x) = 5 f(x) - 4
In other words, I do not know the answer based on the question.
To find the value of g(6), we need additional information. The given conditions only provide information about f(6), the continuity of f(x) and g(x), and the limit of (5f(x) - g(x)) as x approaches 0.
We cannot directly determine g(6) with the given information. However, we can make some observations based on the given conditions.
Since f(x) is continuous and f(6) = 3, we can state that the function f(x) is continuous at x = 6. This means that the value of f(x) does not have any jumps, holes, or vertical asymptotes at x = 6.
Regarding the limit of (5f(x) - g(x)) as x approaches 0, we know that the limit is equal to 4. Therefore, we can write this as an equation:
lim(x->0) (5f(x) - g(x)) = 4
Now, using algebraic manipulation, we can rewrite this equation as:
5 * lim(x->0) f(x) - lim(x->0) g(x) = 4
Since f(x) is continuous and the limit exists as x approaches 0, we can replace lim(x->0) f(x) with f(0):
5 * f(0) - lim(x->0) g(x) = 4
However, this equation still does not provide any direct information about g(6).
In conclusion, based on the given conditions, we cannot determine the value of g(6) without additional information about g(x) or an equation involving g(x) explicitly.