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Thread: How do I solve for F(1) given a piecewise function with a missing variable?

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    How do I solve for F(1) given a piecewise function with a missing variable?

    How do I solve for F(1) given a piecewise function with a missing variable?-help.png
    Hi everyone,

    I am really stumped on this problem and shouldn't be. It seems easy but I cannot get the right answer. Any explanation would be much appreciated! Thank you.
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
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    Hi everyone,

    I am really stumped on this problem and shouldn't be. It seems easy but I cannot get the right answer. Any explanation would be much appreciated! Thank you.
    For a function to be continuous then the function has to be only one value at x = 2, doesn't it? (Ie. $\displaystyle \lim_{x \to 2^{-}} f(x) = \lim_{x \to 2^{+}} f(x)$). So what value do we have to have for c?

    -Dan
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by topsquark View Post
    For a function to be continuous then the function has to be only one value at x = 2, doesn't it? (Ie. $\displaystyle \lim_{x \to 2^{-}} f(x) = \lim_{x \to 2^{+}} f(x)$). So what value do we have to have for c?

    -Dan
    I just figured it out! What I did was set cx+5 = 2x^2 - 5 and solved for C. Then once I had c (turns out to be 2x-10) I inserted 2 for X because they must be the same at X like you said. Wish I did this before wasting two tries on the problem and loosing points. But hey, what can you do!
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
    I just figured it out! What I did was set cx+5 = 2x^2 - 5 and solved for C. Then once I had c (turns out to be 2x-10) I inserted 2 for X because they must be the same at X like you said. Wish I did this before wasting two tries on the problem and loosing points. But hey, what can you do!
    Here is the function.
    $f(x) = \left\{ \begin{gathered}
    cx + 5,\quad x < 2 \hfill \\
    2{x^2} - 5,\quad x \geqslant 2 \hfill \\
    \end{gathered} \right.$ Now here is a standard notation: $\displaystyle{\lim _{x \to {c^ \pm }}}f(x ) = f(c\pm)$

    Thus in this question: $f(2-)=2c+5~\&~f(2+)=3$.

    In order to be everywhere continuous we must have $f(2+)=f(2-)$.
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    Member Walagaster's Avatar
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
    I just figured it out! What I did was set cx+5 = 2x^2 - 5 and solved for C. Then once I had c (turns out to be 2x-10) I inserted 2 for X because they must be the same at X like you said. Wish I did this before wasting two tries on the problem and loosing points. But hey, what can you do!
    I'm guessing you haven't figured it out, given what you have written. What did you get for $f(1)$? I suggest you look again at the hints you have been given.
    Thanks from topsquark
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
    I just figured it out! What I did was set cx+5 = 2x^2 - 5 and solved for C. Then once I had c (turns out to be 2x-10) I inserted 2 for X because they must be the same at X like you said. Wish I did this before wasting two tries on the problem and loosing points. But hey, what can you do!
    You could learn the definitions from the start!
    Thanks from topsquark
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by Walagaster View Post
    I'm guessing you haven't figured it out, given what you have written. What did you get for $f(1)$? I suggest you look again at the hints you have been given.
    Well, I got 4, but now looking at it the next I am not sure how the heck I got to 4.
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by HallsofIvy View Post
    You could learn the definitions from the start!
    I am a human, I cannot remember everything.
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
    I am a human, I cannot remember everything.
    You'll get used to them as they come along. However continuity is a BIG one. Make sure you get the concept down.

    -Dan
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    Forum Admin topsquark's Avatar
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
    I just figured it out! What I did was set cx+5 = 2x^2 - 5 and solved for C. Then once I had c (turns out to be 2x-10) I inserted 2 for X because they must be the same at X like you said. Wish I did this before wasting two tries on the problem and loosing points. But hey, what can you do!
    You are checking continuity at x = 2. So 2c + 5 = 8 - 5. What's c?

    Oh! and C and c represent two different variables.

    -Dan
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
    Well, I got 4, but now looking at it the next I am not sure how the heck I got to 4.
    Never mind, I just re-figured it out. Set the two functions equal to each other, substituted in 2 (because they must equal each other), solved for C, then used it to find F(1). F(1) = -1 x 1 + 5 = 4
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    Re: How do I solve for F(1) given a piecewise function with a missing variable?

    Quote Originally Posted by hessman7 View Post
    I am a human, I cannot remember everything.
    There is a difference between remembering everything and remembering what's important. And in a math class the basic definitions (such as the definition of "continuous") are important.
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