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malfutka [58]
3 years ago
10

Books spontaneously catch on fire in temperatures at or above 451, degree Fahrenheit. Write an inequality that is true only for

temperatures (t)(t)left parenthesis, t, right parenthesis at which books spontaneously catch on fire.
Mathematics
1 answer:
Brilliant_brown [7]3 years ago
3 0
For this case, the first thing you should do is define a variable.
 We have then:
 t: temperature (degree Fahrenheit).
 We write then the inequation that adapts to the problem:
 t> = 451
 Answer:
 
an inequality that is true only for temperatures at which books spontaneously catch on fire is:
 
t> = 451
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The functions are inverses; f(g(x)) = x ⇒ answer D

h^{-1}(x)=\sqrt{\frac{x+1}{3}} ⇒ answer D

Step-by-step explanation:

* <em>Lets explain how to find the inverse of a function</em>

- Let f(x) = y

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∵ f(x)=\sqrt{x-3}

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∴ x² = y - 3

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∴ x² + 3 = y

- Change y by f^{-1}(x)

∴ f^{-1}(x)=x^{2}+3

∵ g(x) = x² + 3

∴ f^{-1}(x)=g(x)

∴ <u><em>The functions are inverses to each other</em></u>

* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

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∴ We will chose the positive value of the square root

∴ \sqrt{\frac{x+1}{3}}=y

- replace y by h^{-1}(x)

∴ h^{-1}(x)=\sqrt{\frac{x+1}{3}}

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