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    (Original post by Brudor2000)
    yh but what if it was not definite like (x,X) and it was something like x E R ( x is all real number)
    Then, as far as C3 is concerned, you just need to start using facts of the basic functions involved.

    Like, for f(x) = 3+2e^{-x} we know that this function is valid for x \in \mathbb{R} and the basic function here is e^x

    You should know that e^x >0, hence e^{-x} > 0 (since replacing x with -x has no effect on the range), then mult both sides by 2 to get 2e^{-x} > 0 and finish by adding 3 to both sides hence 3+2e^{-x} > 3 and hence f(x) > 3.

    For a trig function, well, sine/cosine are between -1 and 1 on reals. The rest I can't be bothered to cover.

    (Original post by Kota Dagnino)
    We are talking in the case of linear functions
    Should've said so then. It seemed as if you were generalising, besides that, the notation (f(x),f(X)) wouldn't make much sense if f(x) is a decreasing function. I.e. f(x)=-x on x \in (0,1) then by your notation f(x) \in (0,-1)
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    (Original post by RDKGames)
    Then, as far as C3 is concerned, you just need to start using facts of the basic functions involved.

    Like, for f(x) = 3+2e^{-x} we know that this function is valid for x \in \mathbb{R} and the basic function here is e^x

    You should know that e^x >0, hence e^{-x} > 0 (since replacing x with -x has no effect on the range), then mult both sides by 2 to get 2e^{-x} > 0 and finish by adding 3 to both sides hence 3+2e^{-x} > 3 and hence f(x) > 3.

    For a trig function, well, sine/cosine are between -1 and 1 on reals. The rest I can't be bothered to cover.


    Should've said so then. It seemed as if you were generalising, besides that, the notation (f(x),f(X)) wouldn't make much sense if f(x) is a decreasing function. I.e. f(x)=-x on x \in (0,1) then by your notation f(x) \in (0,-1)
    that was really helpful! thank u!!
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    Thank you so much @RDKGames, @Anonymouspsych, @Kota Dagnino for your help. I think i get it now. Thanks again!!
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    for exponential functions, things change a little.
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    The first function is the natural logarithm, the second function is the exponential function. Give me a sec i do the trig function
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    These are the classic trig functions
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    Thanks @kota Dagnino
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    No problem
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    (Original post by RDKGames)
    Then, as far as C3 is concerned, you just need to start using facts of the basic functions involved.

    Like, for f(x) = 3+2e^{-x} we know that this function is valid for x \in \mathbb{R} and the basic function here is e^x

    You should know that e^x >0, hence e^{-x} > 0 (since replacing x with -x has no effect on the range), then mult both sides by 2 to get 2e^{-x} > 0 and finish by adding 3 to both sides hence 3+2e^{-x} > 3 and hence f(x) > 3.

    For a trig function, well, sine/cosine are between -1 and 1 on reals. The rest I can't be bothered to cover.


    Should've said so then. It seemed as if you were generalising, besides that, the notation (f(x),f(X)) wouldn't make much sense if f(x) is a decreasing function. I.e. f(x)=-x on x \in (0,1) then by your notation f(x) \in (0,-1)
    Useful, thank you!
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    (Original post by Kota Dagnino)
    Here is another example witten another way
    Careful as, let:

     \displaystyle f(x) = -x+6.

    Then if (as you say):

     \displaystyle x > 3, \, f(x) > f(3) ?

    As this is a decreasing function:

     \displaystyle f(3) = 3, \, f(4) = 2.
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    (Original post by Brudor2000)
    ohh ok. so what would the domain be for the eqn u have given?
    The domain for my function would be

    x∈ ℝ, x≠-1
 
 
 
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