Mathematics: The reward is 20 ! confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = ((x - 7) / (x + 3)) g(x) = - 7) / (x - 1))this is too complicated fort-t

The reward is 20 ! confirm that f and g are inverses

Ответ:

geo58

13.03.2022

Mathematics

Good use of parentheses in asking the question; fellow questioners take note.

$f(x) = \dfrac{x - 7}{x+3}$

$g(x) = \dfrac{-3x - 7}{x-1}$

It looks like we have some algebra ahead of us:

$f(g(x)) = f \left( \dfrac{-3x - 7}{x-1} \right) = \dfrac{ \left( \dfrac{-3x - 7}{x-1} \right) - 7}{ \left( \dfrac{-3x - 7}{x-1} \right)+3}$

When we have a complicated fraction like that it's best if we multiply top and bottom by the inner denominators to simplify:

$f(g(x)) = \dfrac{ \left( \dfrac{-3x - 7}{x-1} \right) - 7}{ \left( \dfrac{-3x - 7}{x-1} \right)+3} \cdot \dfrac{x-1}{x-1} = \dfrac{ (-3x - 7) -7(x-1)}{(-3x - 7)+3(x-1)}$

$f(g(x)) = \dfrac{ -3x -7 -7x+7}{-3x - 7+3x-3} = \dfrac{-10 x}{-10} = x \quad\checkmark$

OK, now the other way.

$g(f(x)) = g \left( \dfrac{x - 7}{x+3} \right) = \dfrac{-3 \left( \dfrac{x - 7}{x+3} \right) - 7}{ \left( \dfrac{x - 7}{x+3} \right)-1} \cdot \dfrac{x+3}{x+3}$

$g(f(x)) = \dfrac{-3(x - 7) - 7(x+3)}{ (x - 7)-(x+3)} = \dfrac{-3x+21-7x-21}{-10} = x \quad\checkmark$

Not so bad.

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Ответ:

bella6786

07.05.2020

Mathematics

Step-by-step explanation:

The scale factor of ABC to DEF is the number you need to multiply a corresponding side of ABC to get one of DBC. We are given the two triangles are similar, so we can say that sides AB and DE are proportional. We are looking for the number we need to multiply AB by to get DE. From this relation, we can get the equation:

AB * x = DE

where x is our scale factor. We can substitute in the values of AB and DE, and solve for x:

5x = 15

x = 3

Therefore, the scale factor is three. This means that you can multiply any side of ABC by 3 to get a side of DEF.

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The reward is 20 ! confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = ((x - 7) / (x + 3)) g(x) = - 7) / (x - 1))this is too complicated fort-t

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