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Alex17521 [72]
3 years ago
7

Solve for x. Express the answer in simplest form. 2/1 = 8x - 2/ 9

Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
4 0
2=8x-2/9
add 2/9 to both sides
2 and 2/9=8x
2=18/9
2 and 2/9=18/9+2/9=20/9
20/9=8x
multiply both sides by 9
20=72x
divide boht isdes by 72
20/72=x=5/18
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Inverse Function In Exercise,analytically show that the functions are inverse functions.Then use the graphing utility to show th
DanielleElmas [232]

Answer:

g^{-1}(x)=f(x)=e^{\frac{x}{3}}

Step-by-step explanation:

We have been given two functions as g(x)=\text{ln}(x^3) and f(x)=e^{\frac{x}{3}}. We are asked to show that both functions are inverse of each other algebraically and graphically.

Let us find inverse function of g(x)=\text{ln}(x^3) as:

y=\text{ln}(x^3)

Interchange x and y values:

x=\text{ln}(y^3)

Using log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

x=3\cdot \text{ln}(y)

\frac{x}{3}=\frac{3\cdot \text{ln}(y)}{3}

\frac{x}{3}=\text{ln}(y)

Using log definition; If \text{log}_a(b)=c, then b=a^c, we will get:

y=e^{\frac{x}{3}}

g^{-1}(x)=e^{\frac{x}{3}}

Therefore, we can see that function f(x)=e^{\frac{x}{3}} is inverse of function g(x)=\text{ln}(x^3).

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8 0
4 years ago
Solve this equation.<br> 5x-2y=3<br> y=2x
insens350 [35]

Answer:

3

Step-by-step explanation:

5x-2y=3  when: y=2x

1. Plug in the y-value (y=2x) into the equation (5x-2y=3). The equation should then look like 5x-2(2x)=3

2. Simplify:

5x-2(2x)=3

5x-4x=3

1x=3

x=3

Check:

5x-2(2x)=3 (plug in the x-value you solved for: 3)

5(3)-2×2(3)=3

15-2×6=3

15-12=3

3=3

Hope this helped !

Cheers, Z

8 0
3 years ago
Factor the expression completely over the complex numbers. <br><br> x^3-4x^2+4x-16
Orlov [11]

First you must know that is i∧2= -1

x∧3-4x∧2+4x-16 = x∧2 (x-4) + 4 (x-4) = (x-4) (x∧2+4) = (x-4) (x∧2-(-4)) =

= (x-4) (x∧2-(-1) *4) = (x-4) (x∧2- i∧2*2∧2) = (x-4) (x∧2-(2i)∧2) = (x-4) (x-2i) (x+2i)

Good luck!!!

5 0
3 years ago
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