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3 years ago

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

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]

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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:

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

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