Determine the domain of the function.

1 answer:

4 0

We are given with a verbal phrase of a function<span> of x is equal to the square root of x plus one divided by x plus four times x minus six.

This is expressed as f(x) = </span>√(x) + 1/x + 4x - 6
the domain are values which include only natural numbers because of the square root sign. answer is D. <span>x ≥ 0</span>

You might be interested in

Solve the simultaneous equations<br> 3<br> 2x - y = 7<br> xy = 15

ehidna [41]

Answer:

(5, 3 ) and (- $\frac{3}{2}$ , - 10 )

Step-by-step explanation:

Given the 2 equations

2x - y = 7 → (1)

xy = 15 → (2)

Rearrange (1) expressing y in terms of x , that is

y = 2x - 7 → (3)

Substitute y = 2x - 7 into (2)

x(2x - 7) = 15

2x² - 7x = 15 ( subtract 15 from both sides )

2x² - 7x - 15 = 0 ← in standard form

(x - 5)(2x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - $\frac{3}{2}$

Substitute these values into (3) for corresponding values of y

x = 5 : y = 2(5) - 7 = 10 - 7 = 3 ⇒ (5, 3 )

x = - $\frac{3}{2}$ : y = 2(- $\frac{3}{2}$ ) - 7 = - 3 - 7 = - 10 ⇒ (- $\frac{3}{2}$ , - 10 )

8 0

2 years ago

Use a graphing utility to graph the function and visually estimate the limits.

levacccp [35]

The value of the $\lim_{x \to 0} f(x)$ and $\lim_{x \to \frac{\pi }{3} } f(x)$ are 0 and 1.153 .

<h3></h3><h3>What is the limiting value of a function?</h3>

Limiting Value of a Function. The function's limit is the value of the function as its independent variable, such as x approaches a certain value called the limiting value. For simple equations, this is similar to finding out the value of y when x has a unique value.

Given that,

f(x) = $4x cos x$