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wolfram-mathematicawolframalpha

Wolfram Alpha functions and plots

I am new with wolfram alpha and I am trying to do the following but I am having trouble doing it.

(1) On Wolfram Alpha, how can we plot two inequalities on the same graph? For example, if I want to plot x^3>-1 and x^2 - 1 < 0

(2) On Wolfram Alpha, how can we use the If function to impose restrictions on variables. For example, I want to ask "If x>0, is 4^x < 3 ^(x+1) ? How do I impose the constraint "x>0"?

Any help would be appreciated. Thank you.

Solution

  • First one:

    solve x^3 > -1 && x^2 - 1 < 0

    -1 < x < 1

    Second one:

    4^x < 3^(x + 1) && x > 0

    (0, -log(3)/(log(3) - 2 log(2))

    I.e. true between 0 and 3.81884