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leonid [27]
3 years ago
12

Given that f(a+b)= f(a) + f(b) and f(x) is always positive, what os the value of f(0)?

Mathematics
1 answer:
FrozenT [24]3 years ago
4 0
This is a strange question, and f(x) may not even exist. Why do I say that? Well..

[1] We know that f(a+b) = f(a) + f(b). Therefore, f(0+0) = f(0) + f(0). In other words, f(0) = f(0) + f(0). Subtracting, we see, f(0) - f(0) = f(0) or 0 = f(0).

[2] So, what's the problem? We found the answer, f(0) = 0, right? Maybe, but the second rule says that f(x) is always positive. However, f(0) = 0 is not positive!

Since there is a contradiction, we must either conclude that the single value f(0) does not exist, or that the entire function f(x) does not exist.

To fix this, we could instead say that "f(x) is always nonnegative" and then we would be safe.
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3 years ago
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5 0
2 years ago
Choose the function whose graph is given by:
wolverine [178]

<em>Greetings from Brasil...</em>

In a trigonometric function

F(X) = ±UD ± A.COS(Px + LR)

UD - move the graph to Up or Down (+ = up | - = down)

A - amplitude

P - period (period = 2π/P)

LR - move the graph to Left or Right (+ = left | - = right)

So:

A) F(X) = COS(X + 1)

standard cosine graph with 1 unit shift to the left

B) F(X) = COS(X) - 1 = -1 + COS(X)

standard cosine graph with 1 unit down

C) F(X) = COS(X - 1)

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D) F(X) = SEN(X - 1)

standard Sine graph with shift 1 unit to the right

Observing the graph we notice the sine function shifted 1 unit to the right, then

<h3>Option D</h3>

<em>(cosine star the curve in X and Y = zero. sine start the curve in Y = 1)</em>

7 0
3 years ago
Read 2 more answers
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