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3 years ago

Which of the following equations represents the inverse of y = e2x - 9?

Mathematics

2 answers:

Marysya12 [62]3 years ago

8 0

Answer:

y=1/2 (Inx+9)

skelet666 [1.2K]3 years ago

4 0

Important: write this function as y = e^(2x) - 9. " ^ " indicates exponentiation.

To find the inverse function:

1) interchange x and y. y becomes x and x becomes y: x = e^(2y) - 9
2) solve this result for y:

e^(2y) = x + 9 Take the natural log of both sides:

2y = ln(x+9) (domain is restricted to "x is greater than -9")

ln(x+9)
Then y = -----------
2

This is the inverse function of y = e^(2x) - 9.

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Leni [432]

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3>Solution:</h3>

a. The points (-4,1) and (2,4) both lie on the line

The general line equation on which (a, b) and (c, d) lies is:

$y-\mathrm{b}=\frac{d-b}{c-a}(x - a)$

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

$y-1=\frac{4-1}{2-(-4)}(x-(-4))$

On solving we get,

$\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}$

b.) m= -1 and the point (2, -1) lies on the line

The equation of line in point slope form is y – b = m(x – a)

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)

y + 1 = -x + 2

y = -x + 2 -1

y = -x + 1

c. )It has the same slope as y = 5 and passes through (1, 1)

our line has same slope with y = 5, then our equation would be y = k and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1

Then our equation will be y = k

y = 1

d. ) m= -3 and it has a y-intercept of (0, 8)

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

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3 years ago

What is the correct answer can you guys help me I really need help on this?? Please

luda_lava [24]

The answer is 192 y^8.

(4y^2)^3 = 64y^6

64y^6 • 3y^2= 192y^8

When “multiplying” a number with an exponent, you add the 2 exponents.

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4 years ago