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Elis [28]
3 years ago
14

1\tfrac{2}{5} \div \frac{8}{9} 1 5/2 ÷ 9/8

Mathematics
1 answer:
Alexandra [31]3 years ago
5 0

Answer:

Step-by-step explanation:

What you wrote below the top line and the bottom line are not the same thing.

I think you really want the second line, but one can't be sure.

(1*2 + 5)/2 div (9/8)

7/2 // 9/8

7/2 * 8*9

7*8/18 = 56/18 = 28/9

If you really do want the top line (the latex) it is different.

1 2/5  div (8/9)     Is there such a thing as tfrac? I didn't know this but there is.

(1*5 + 2)5 // (8/9)

7/5 // 8/9             Invert the bottom fraction and multiply

7/5 * 9 / 8

63 / 40

1 23/40

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Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

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Step-by-step explanation:

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

- Let f(x) = y

- Exchange x and y

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- The new y = f^{-1}(x)

* <em>Lets use these steps to solve the problems</em>

∵ f(x)=\sqrt{x-3}

∵ f(x) = y

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- Exchange x and y

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∴ x² = y - 3

- Add 3 to both sides

∴ 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)

∵ f(x)=\sqrt{x-3}

∵ g(x) = x² + 3

∴ f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x

∴ <u><em>f(g(x)) = x</em></u>

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* <em>Lets find the inverse of h(x)</em>

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

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- Exchange x and y

∴ x = 3y² - 1

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- Take √ for both sides

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∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ \sqrt{\frac{x+1}{3}}=y

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

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