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When comparing the f(x) = x^2 – x and g(x) = log(2x + 1), on which interval are both functions positive?(–∞, 0) (0, 1) (1, ∞) (∞, ∞)

User Cncool
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(1\text{ , }\infty)

Step-by-step explanation:

Since for g(-∞), is not a possible answer. we remove it.

We also remove (∞,∞), because it goes back to being simply ∞.

Now for

(0 , 1 )


\begin{gathered} f(x)\text{ = x}^2\text{ - x } \\ f(1)\text{ = 1}^2\text{ - 1 = 0} \end{gathered}


f(0)\text{ = 0}^2\text{ - 0 = 0}

This is not positive, nor negative so we will also put this one on the side.

For the last interval (1, ∞)


\begin{gathered} f(1)\text{ = 0 } \\ f(\infty)\text{ = }\infty^2-\infty\text{ = }\infty \end{gathered}

=> f(x) is positive


g(1)\text{ = log\lparen2*1 + 1\rparen = log\lparen3\rparen }\approx\text{ 0.477712}

g(1) is positive


g(\infty)\text{ = log\lparen2*}\infty+1)\text{ = log\lparen}\infty)\text{ = }\infty

=> g(∞) is positive

Hence f(x) and g(x) are both positve on the interval (1, 8)

NB:

Technically you should say g(x) tend to infinity (or a approaches infinity) not is equal to infinity, because infinity is not a number

User Sayantan Das
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