3 years ago

Which of the following is equivalent to log9w

Mathematics

1 answer:

liraira [26]3 years ago

6 0

what do you meanAnswer:

Step-by-step explanation:

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Find the inverse function (find f^-1)

Reil [10]

Step-by-step explanation:

f(x) = (x-2)/(3x+3). Let y = f(x).

Then y = (x-2)/(3x+3).

y(3x+3) = x - 2

3xy + 3y = x - 2

3xy - x = -3y - 2

x(3y-1) = -(3y+2)

x = -(3y+2)/(3y-1)

Hence, the inverse of f(x) is -(3x+2)/(3x-1).

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B%282x%2B1%29%28x-5%29%7D%7B%28x-5%29%28x%2B4%29%5E%7B2%7D%20%7D" id

dybincka [34]

i) The given function is

$f(x)=\frac{(2x+1)(x-5)}{(x-5)(x+4)^2}$

The domain is

$(x-5)(x+4)^2\ne 0$

$(x-5)\ne0,(x+4)^2\ne 0$

$x\ne5,x\ne -4$

ii) For vertical asymptotes, we simplify the function to get;

$f(x)=\frac{(2x+1)}{(x+4)^2}$

The vertical asymptote occurs at

$(x+4)^2=0$

$x=-4$

iii) The roots are the x-intercepts of the reduced fraction.

Equate the numerator of the reduced fraction to zero.

$2x+1=0$

$2x=-1$

$x=-\frac{1}{2}$

iv) To find the y-intercept, we substitute $x=0$ into the reduced fraction.

$f(0)=\frac{(2(0)+1)}{(0+4)^2}$

$f(0)=\frac{(1)}{(4)^2}$

$f(0)=\frac{1}{16}$

v) The horizontal asymptote is given by;

$lim_{x\to \infty}\frac{(2x+1)}{(x+4)^2}=0$

The horizontal asymptote is $y=0$ .

vi) The function has a hole at $x-5=0$ .

Thus at $x=5$ .

This is the factor common to both the numerator and the denominator.

vii) The function is a proper rational function.

Proper rational functions do not have oblique asymptotes.

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3 years ago

How do I do number 8?

Tatiana [17]

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4 years ago

What is the percent composition of C4H10?

horsena [70]

82.7% = C and 17.3% = H

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Which equation would be the equation that has a slope at 4 and passes through the point (2, 10)? y = 4x + 2 y = 8x + 18 y = 4x -

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3 years ago