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alexdok [17]
3 years ago
9

F(x) = 5/(7x-8) What is the inverse of this function?

Mathematics
2 answers:
oee [108]3 years ago
3 0
f(x)=\dfrac{5}{7x-8}\\\\y=\dfrac{5}{7x-8}\iff\dfrac{1}{y}=\dfrac{7x-8}{5}\ \ \ |multiply\ both\ sides\ by\ 5\\\\\dfrac{5}{y}=7x-8\ \ \ |add\ 8\ to\ both\ sides\\\\7x=\dfrac{5}{y}+8\\\\7x=\dfrac{5}{y}+\dfrac{8y}{y}\\\\7x=\dfrac{5+8y}{y}\ \ \ \ |divide\ both\ sides\ by\ 7\\\\x=\dfrac{5+8y}{7y}\\\\Answer:\boxed{f^{-1}(x)=\dfrac{5+8x}{7x}\ other\ form\ f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}
zzz [600]3 years ago
3 0
f(x)=\dfrac{5}{7x-8}\\
y=\dfrac{5}{7x-8}\\
7x-8=\dfrac{5}{y}\\
7x=\dfrac{5}{y}+8\\
x=\dfrac{5}{7y}+\dfrac{8}{7}\\
\boxed{f^{-1}(x)=\dfrac{5}{7x}+\dfrac{8}{7}}

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Julli [10]

Answer:

x = 3 and 7

There are two true solutions.

Step-by-step explanation:

To solve x-7 = \sqrt{-4x+28}, use inverse operations by squaring both sides of the equal sign.

(x-7)^2 = (\sqrt{-4x+28})^2\\x^2-14x+49 = -4x+28\\x^2-14x+4x+49-28 = 0\\x^2-10x+21=0

The quadratic expression can be factored into binomials and set equal to 0 by the zero product property to find x.

(x - 3) ( x - 7) = 0

x-3 = 0 so x=3

x-7 = 0 so x=7

Now check each solution into the original equation to be sure it solve the solution and is not extraneous.

7-7 = \sqrt{-4(7)+28}\\ 0=0

and

3-7 = \sqrt{-4(3)+28}\\[tex]-4 = \sqrt{16}\\-4 =-4[/tex]

3 0
3 years ago
Bonnie is making a dipping sauce. She mixes 150 milliliters of soy sauce with 100 milliliters of vinegar. How much soy sauce doe
oksian1 [2.3K]

Answer:

Bonnie is mixing 1.50 milliliter of soy sauce with 1 milliliter of vinegar

Step-by-step explanation:

Given

Bonnie mixes 150 milliliters of soy sauce with 100 milliliters of vinegar

So, in order to find the amount of soy sauce mixed with one ml of vinegar, we have to divide the amount of soy sauce by vinegar.

So,

Soy\ sauce\ mixed\ with\ 1\ ml\ of\ vinegar\ =\frac{150}{100}\\ = \frac{3}{2}\\=1.50

Hence,

Bonnie is mixing 1.50 milliliter of soy sauce with 1 milliliter of vinegar

3 0
3 years ago
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sasho [114]
It would be 8 to the 8th power
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Alexxx [7]

Answer:

71

Step-by-step explanation:

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3 years ago
What is the nth term rule of the linear sequence below? 15 , 7 , − 1 , − 9 , − 17 , . . .
Doss [256]

You can see that you're constantly subtracting 8 to get the next number. So, we have

a_1 = 15

a_2 = a_1-8

a_3 = a_2-8 = (a_1-8)-8=a_1-2\cdot 8

a_4=a_1-3\cdot 8

a_5=a_1-4\cdot 8

So, as you can see, to get the n-th term we must subtract (n-1) times 8 from the original number.

7 0
3 years ago
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