What does f(-5)=-2 tell me about f(x)

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You miss understand.

$f$ is a function, say $f$ is $f(x)$. For example consider $f(x)=x+3$, then $$f(-5)=-5+3=-2$$ but $f$ is not identically $-2$ because for example $f(0)=3$.

Now, $g(x)=-2f(x)$, for what $x$ can you compute $g(x)$ ?

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Merlin's Beard
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Merlin's Beard

Updated on September 07, 2020

Comments

  • Merlin's Beard
    Merlin's Beard about 3 years

    As part of a math quiz I was given the following two functions:

    f(-5) = -2 and g(x) = -2 * f(x)

    The way I interpret the first function is "return -2 regardless of the input" since the right hand side is just a constant. That would mean that f(x) will also result in -2, making the result of g(x) positive 4.

    But I guess I'm missing something because that is not one of the available answers in the quiz.


    Edit:

    Apologies for the unclear question.

    The full question in the quiz is as follows:

    If $f(−5) = −2$ and $g(x) = −2 \cdot f(x)$, what point can you determine on the graph of $g$?

    I realize now my interpretation was wrong. Like André said in the comment: I only know the output (-2) of a given input (-5). Knowing how to read the function f helped me solve the question, thanks guys.

    • Crostul
      Crostul about 9 years
      What is your question?
    • Paul Sundheim
      Paul Sundheim about 9 years
      You were given the functions, but what question about the functions did they pose? It is true that $g(-5)=4$ but that doesn't mean that $g(x)=4$.
    • André Nicolas
      André Nicolas about 9 years
      The interpretation of the function $f$ is not right. All the equation says is "return $-2$ on input $-5$." It says nothing about what to return for other inputs.
  • Merlin's Beard
    Merlin's Beard about 9 years
    Thanks for the nice explanation.
  • Asaf Karagila
    Asaf Karagila about 9 years
    I think the correct word is "misunderstand" and not "miss understand" (who is the daughter of Mr. and Mrs. Understand :-P).