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3 years ago

Let f(x)=3x-6. Is f one-to-one? If it is find f^-1, if not explain why.

Mathematics

1 answer:

beks73 [17]3 years ago

8 0

Answer: Yes, $\bold{f^{-1}(x)=\dfrac{x+6}{3}}$

Step-by-step explanation:

f(x) = 3x - 6 is a line so it is a function because

it passes the vertical line test

and the horizontal line test

To find the inverse, swap the x's and y's and solve for y

$y=3x-6\\\\\\\text{Swap the x's and y's:}\qquad x=3y-6\\\\\text{Add 6 to both sides:}\qquad x+6=3y\\\\\text{Divide both sides by 3:}\qquad \dfrac{x+6}{3}=y$

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Katen [24]

$\green{\large\underline{\sf{Solution-}}}$

Given expression is 

$\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} }$

can be rewritten as

$\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} }$

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\$

And

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\$

So, using this identity, we

$\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} }$

can be further rewritten as

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)}$

$\rm \: = \: \dfrac{4}{25 - 1}$

$\rm \: = \: \dfrac{4}{24}$

$\rm \: = \: \dfrac{1}{6}$

Hence, 

$\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}$

4 0

2 years ago

Write the expression as the logarithm of a single number or expression. 4 In 2+3 In 5

madreJ [45]

Answer:

ln [2^4 * 5^3]

Step-by-step explanation:

Rewrite 4 ln 2 as ln 2^4 and 3 ln 5 as ln 5^3.

Then 4 In 2+3 In 5 = ln 2^4 + ln 5^3, which in turn becomes

ln [2^4 * 5^3]

6 0

3 years ago

mars1129 [50]

Answer:

yes they are

Step-by-step explanation:

they are both congruent because they are the same shape and size, they are just on opposite sides

(congruent means that 2 objects are the same shape and size)

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3 years ago

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Naily [24]

Answer: -2

Step-by-step explanation:

f(-2) = -2

It is the value of y when x = -2. I read "-2."

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2 years ago

What is the solution to the equation? c/23 = 2/3

k0ka [10]

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3 years ago

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