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4 years ago

HELPPP I WILL BRAINLIST!!

Mathematics

1 answer:

charle [14.2K]4 years ago

3 0

Answer:

Step-by-step explanation:

8 (x -3) +7 = 2x (4 -17)

8(x -3) +7 = 2x (-13) here was the error because the had 13 that is incorrect

8x -24 +7 = -26x

8x -17 = -26x

-17 = -26x -8x

-17 = -34x

-17/-34 = x

1/2 =x

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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:

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

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

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

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 $g(x)=\text{ln}(x^3)$ .

We can see that both functions are symmetric about line $y=x$ , therefore, both functions are inverse of each other.

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