All categories

3 years ago

Given f(x)=1/x+3 and g(x)=6/x+4, find the domain of f(g(x))

Mathematics

1 answer:

Murljashka [212]3 years ago

4 0

Answer:

The domain is all real numbers except the value of x=-6

Step-by-step explanation:

we have

$f(x)=\frac{1}{x+3}$

$g(x)=\frac{6}{x+4}$

we know that

$f(g(x))=\frac{1}{(\frac{6}{x+4})+3}$

$f(g(x))=\frac{1}{\frac{6+3(x+4)}{x+4}}$

$f(g(x))=\frac{x+4}{6+3x+12}$

$f(g(x))=\frac{x+4}{3x+18}$

$f(g(x))=\frac{x+4}{3(x+6)}$

Remember that the denominator cannot be equal to zero

The value of x cannot be equal to -6

therefore

The domain is all real numbers except the value of x=-6

In interval notation the domain is

(-∞,-6) ∪ (-6,∞)

You might be interested in

Please help with this AP Calculus question !

melomori [17]

Answer:

C. $\displaystyle \frac{cos(x)}{x} - ln(x)sin(x)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Trig Derivatives

Logarithmic Derivatives

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = ln(x)cos(x)$

Step 2: Differentiate

Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[ln(x)]cos(x) + ln(x)\frac{d}{dx}[cos(x)]$
Logarithmic Derivative: $\displaystyle f'(x) = \frac{1}{x}cos(x) + ln(x)\frac{d}{dx}[cos(x)]$
Trig Derivative: $\displaystyle f'(x) = \frac{1}{x}cos(x) + ln(x)[-sin(x)]$
Simplify: $\displaystyle f'(x) = \frac{cos(x)}{x} - ln(x)sin(x)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

7 0

3 years ago

Factor the following equation to find its zeros.

Thepotemich [5.8K]

Answer:

A| 12, 3

Step-by-step explanation:

The polynomial can be factored by looking for factors of 36 that sum to -15. The sum being negative while the product is positive means both factors will be negative. The answer choices suggest ...

y = (x -12)(x -3)

A quick check shows this product is ...

y = x^2 -12x -3x +36 = x^2 -15x +36 . . . . as required

The factors are zero when x is either 12 or 3.

The zeros of the equation are 12 and 3.

____

Once you realize the constants in the binomial factors both have a negative sign, you can immediately choose the correct answer (A).

Or, you can use Descartes' rule of signs, which tells you that the two sign changes in the coefficients (+-+) mean there are 2 positive real roots.

6 0

3 years ago

Write the following numbers used in these statements in scientific notation. (Note: Some of these numbers have been rounded.)

lutik1710 [3]

Answer:

So in scientific form 4000 miles will be equal to $4\times 10^3miles$

Step-by-step explanation:

We have given that radius of earth is 4000 miles

4000 miles can be written as 4×1000

We have to written 4000 miles in scientific form

We know that 1000 can be written in scientific form as $1000=10^3$

So $4000miles =4\times 1000=4\times 10^3miles$

So in scientific form 4000 miles will be equal to $4\times 10^3miles$

5 0

3 years ago

NEED HELP WITH THESE QUESTIONS

amm1812

For this case we must solve the following questions:

Question 1:

We should simplify the following expression:

$\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =$

Applying double C we have:

$\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =$

By definition of multiplication of powers of the same base we have to place the same base and add the exponents: $\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =$