What's the equivalent to x=ln(y)

Determine the domain of the function (fog) (x) where f(x) = 3x-1/x-4 and g(x)=x+1/x

Mrac [35]

Answer:

$(-\infty,0)\cup(0, \frac{1}{3})\cup (\frac{1}{3},\infty)$

Step-by-step explanation:

The given functions are $f(x)=\frac{3x-1}{x-4}$ and $g(x)=\frac{x+1}{x}$ .

We now composed the two functions to find:

$(f\circ g)(x)=f(g(x))$

$\implies (f\circ g)(x)=f(\frac{x+1}{x})$

$\implies (f\circ g)(x)=\frac{3(\frac{x+1}{x})+1}{\frac{x+1}{x}-4}$

$\implies (f\circ g)(x)=\frac{4x+3}{1-3x}$

This function is defined if the denominator is not zero.

$1-3x\ne0$

$x\ne\frac{1}{3}$

We write this in interval notation as:

$(-\infty,\frac{1}{3})\cup (\frac{1}{3},\infty)$

We need to be cautious here as x=0 is not in the domain of g(x).

Therefore the domain of $(f\circ g)(x)$ is

$(-\infty,0)\cup(0, \frac{1}{3})\cup (\frac{1}{3},\infty)$

4 0

3 years ago

What is Australia constitution

Daniel [21]

Answer :

The Australian Constitution is the set of rules by which Australia is run. It came into effect on 1 January 1901. This fact sheet summarises the key features of the Constitution and how it can be changed. Commonwealth of Australia Constitution Act, 1900: Original Public Record Copy (1900).

7 0

2 years ago

Solve.

Nat2105 [25]

The solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5

Given the algebraic equation, −0.4x−3.1 = 5.9, to solve for x, follow the steps below:

−0.4x − 3.1 = 5.9

Add 3.1 to both sides

−0.4x − 3.1 + 3.1 = 5.9 + 3.1

-0.4x = 9

Divide both sides by -0.4

-0.4x/-0.4 = 9/-0.4

x = -22.5

Therefore, the solution to the algebraic equation, −0.4x − 3.1 = 5.9, is: x = -22.5

Learn more here:

brainly.com/question/16864747

7 0

2 years ago

Many insects migrate (travel) between their summer and winter homes. The desert locust migrates about 800 miles farther than the

Harman [31]

Answer:

Distance travelled by Monarch butterfly = 2000 miles

Distance travelled by desert locust = 2800

Distance travelled by pink-spotted hawk moth= 7800 miles

Step-by-step explanation:

Let the distance travelled by Monarch butterfly be "X" miles

Distance travelled by desert locust is equal to X + 800 miles

Distance travelled by pink-spotted hawk moth is equal to 4X -200 miles

The total distance travelled by the three is equal to 12600 miles

$X + X + 800 + 4X -200 = 12600\\6X = 12600 -600\\6X = 12000\\X = 2000$

Distance travelled by Monarch butterfly = 2000 miles

Distance travelled by desert locust = 2000 + 800 = 2800

Distance travelled by pink-spotted hawk moth = 4 * 2000 -200 = 7800 miles

6 0

3 years ago

Find the sum of the first 30 terms of the equation below: an=4n+1

Alex73 [517]

Let n = 30

We are actually looking for a_30.

a_30 = 4(30) + 1

a_30 = 120 + 1

a_30 = 121

6 0

3 years ago

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