#Calculus Question Help Needed.

34 messages · Page 1 of 1 (latest)

unkempt groveBOT
sharp mango
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<@&286206848099549185>

nocturne dome
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What do you want to ask?

neat storm
sharp mango
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For part a) can I prove it by simply plugging the inverse they have given into the original cosh(x) and if i can show that equals x, i'm done?

neat storm
sharp mango
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Can someone ban this troll?

sharp mango
nocturne dome
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That is one way to do it, yes. But it might be more fun to get your hands dirty and inverting this bad boy on your own. Try the substitutions $y = e^x$ and $y^{-1} = e^{-x}$ and solving for $y$. (Hint: you should get a quadratic equation).

thick duneBOT
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11de784a

605126582616719390.png
sharp mango
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Ok but is this true: the definition of an inverse function of f(x) is a function g(x) such that f(g(x)) = x ?

sharp mango
nocturne dome
sharp mango
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ok cool

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My other question was

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What is the significance of the domain they have given?

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Because all I need to do is plug in the given inverse to cosh(x) and show it equals x

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Why is that domain they gave important and do I need to use it in an answer?

nocturne dome
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Try to think about what happens when you put a number outside the domain in the expression for $\cosh^{-1}(x)$

thick duneBOT
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11de784a

605126582616719390.png
sharp mango
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ah

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it would be ln of a negative which is undefined

nocturne dome
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It would be the square root of a negative wrong statement, ignore.

sharp mango
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ok, so that is why they said that, but i don't need to restate that domain right? It's just given for valid input purposes.

sharp mango
nocturne dome
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There is a deeper reason as well.

sharp mango
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It's always x^2 the negative would become positive

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ok ok

nocturne dome
thick duneBOT
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11de784a

605126582616719390.png
sharp mango
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x can't be negative

nocturne dome
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Do you know the definition of surjective and injective functions?

sharp mango
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no

nocturne dome
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one-to-one and onto functions?