analysis: find a, b, given f(x)={3^(b*x)+2*x , x<=2*a-1, {9*x-4*b*x , x>=a^2

[oana0610]

Determine that a and b knowing that f admits primitives ,f(x)={3^(b*x)+2*x , x<=2*a-1
{9*x-4*b*x , x>=a^2

 

[Deleted member 4993]

Determine that a and b knowing that f admits primitives ,f(x)={3^(b*x)+2*x , x<=2*a-1
{9*x-4*b*x , x>=a^2

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[stapel]

Determine that a and b, given that f admits primitives:

. . . . .\(\displaystyle f(x)\, =\, \begin{cases}3^{bx}\, +\, 2x & x\, \leq\, 2a\, -\, 1 \\ 9x\, -\, 4bx & x\, \geq\, a^2 \end{cases}\)

What do you mean by "admits primitives"? Do you mean that "the function is integrable" (or, which is the same thing, that "the function has an anti-derivative")? (here

Also, is some portion of the real numbers not part of the domain of f? I note that the first listed rule for f is valid over an interval that includes the endpoint, and so also is the second rule. Since a function cannot have f defined two different ways for the same input x, then 2a - 1 cannot equal a^2. Or is one of the posted "or equal to" statements supposed to be "but not equal to"?

When you reply, please include a clear listing of your thoughts and efforts so far, so we can see where you're getting stuck. Thank you!