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Sati [7]
1 year ago
15

If f and g are continuous functions with f(0) = 2 and the following limit, find g(0). lim_(x->0)[2 f(x) - g(x)] = -3

Mathematics
1 answer:
ladessa [460]1 year ago
5 0

We have by distributivity of limits over sums, and continuity of f(x) and g(x), that

\displaystyle \lim_{x\to0} \bigg(2f(x) - g(x)\bigg) = 2 \lim_{x\to0} f(x) - \lim_{x\to0} g(x) = 2 f(0) - g(0)

Given f(0)=2, it follows that

2^2 - g(0) = -3 \implies g(0) = \boxed{7}

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