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matrenka [14]
3 years ago
13

Find a formula for the inverse of the function. f(x) = e^6x − 9

Mathematics
1 answer:
STatiana [176]3 years ago
7 0

Answer:

f^{-1}(x)=\frac{1}{6}\ln(x+9)

Step-by-step explanation:

So we have the function:

f(x)=e^{6x}-9

To solve for the inverse of a function, change f(x) and x, change the f(x) to f⁻¹(x), and solve for it. Therefore:

x=e^{6f^{-1}(x)}-9

Add 9 to both sides:

x+9=e^{6f^{-1}(x)}

Take the natural log of both sides:

\ln(x+9)=\ln(e^{6f^{-1}(x)})

The right side cancels:

\ln(x+9)=6f^{-1}(x)

Divide both sides by 6:

f^{-1}(x)=\frac{1}{6}\ln(x+9)

And we're done!

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julsineya [31]

If she makes $9 per hour and the amount of hours is h, her amount of pay p is equal to 9h, so p = 9h

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8 0
3 years ago
Solve 3x^2=-12x-15 using a quadratic equation with complex solutions
adelina 88 [10]

The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

What is Quadratic equation?

An algebraic equation of the second degree is called a quadratic equation.

Given that;

A quadratic equation is;

3x² = -12x - 15

Now, The equation is written as;

3x² + 12x + 15 = 0

Take 3 common, we get;

3 (x² + 4x + 5) = 0

x² + 4x + 5 = 0

Factorize the equation by using Sridharacharya Formula;

x = - 4 ± √4² - 4*1*5 / 2*1

x = -4 ± √16 - 20 / 2

x = - 4 ± √-4 / 2

Since, √-1 = i

x = -4 ± 2i / 2                            

x = - 2 ± i

It gives two values of x as;

x = - 2 + i

And, x = - 2 - i

Hence, The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

Learn more about the quadratic equation visit:

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5 0
10 months ago
1 tenth of 70kg is if you help thx
kkurt [141]

it would be 70/100 then it would go down to 7/10 so 1/10 of 70kg would be 7kg because you change 70 you make it a decimal witch is .70 or .7 now make that into a fraction and it would be 70/100 or 7/10 then you take your 7 because its 1/10 of 70. Or you could do it a whole lot easier way and just divide 70 by 10 and get 7. There you have it your answer is 7.

                                        HOPE THIS HELPED!!!

                                                   THANKS!!!

8 0
3 years ago
HELP ASAP
vovangra [49]

Answer:

  • See below and the attachment

Step-by-step explanation:

<em>Refer to attached graph.</em>

<em>It i</em>ncludes the points and a best fit line produced by a graphing calculator.

  • 17. The scatter plot is attached
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3 years ago
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