If f and g are continuous functions with f(-1) = 5 and the following limit, find g(-1).
lim_(x->-1)[5 f(x) - g(x)] = 18
To find g(-1), we need to use the given limit and information about f.
From the given limit, we have:
lim_(x->-1)[5 f(x) - g(x)] = 18
Since we are taking the limit as x approaches -1, we can substitute -1 into the equation:
5 f(-1) - g(-1) = 18
Substitute the value we know:
5 (5) - g(-1) = 18
Simplify the equation:
25 - g(-1) = 18
To isolate g(-1), subtract 25 from both sides:
-g(-1) = 18 - 25
-g(-1) = -7
Multiply both sides by -1 to solve for g(-1):
g(-1) = 7
Therefore, g(-1) = 7.
To find g(-1), we can use the given information and the limit provided. Here's how to do it:
1. Given that f(x) is a continuous function, we know that f(-1) = 5. So, f(-1) = 5.
2. We are given the limit as x approaches -1 of [5 f(x) - g(x)] = 18. Let's rewrite this equation:
lim(x->-1) [5 f(x) - g(x)] = 18
3. To find g(-1), we need to substitute x = -1 into the limit equation:
lim(x->-1) [5 f(x) - g(x)] = 18
[5 f(-1) - g(-1)] = 18
4. Substitute the known value of f(-1) = 5 into the equation:
[5 * 5 - g(-1)] = 18
25 - g(-1) = 18
5. Solve the equation for g(-1):
- g(-1) = 18 - 25
- g(-1) = -7
6. Multiply both sides by -1 to isolate g(-1):
g(-1) = 7
Therefore, g(-1) = 7.