21. (01.05)

If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (

Mars2501 [29]

Question:

If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?

h (x) = StartFraction x + 5 Over 11 EndFraction

h (x) = StartFraction 11 Over x minus 1 EndFraction

h (x) = StartFraction 11 Over x minus 4 EndFraction

h (x) = StartFraction 11 Over x minus 3 EndFraction

Answer:

Option C: $h(x)=\frac{11}{x-4}$ has the same domain as $(m \circ n)(x)$

Explanation:

It is given that $m(x)=\frac{x+5}{x-1}$ and $n(x)=x-3$

Let us find the domain of $(m \circ n)(x)$

$\begin{aligned}(m \circ n)(x) &=m(n(x))\\&=m(x-3) \\ &=\frac{(x-3)+5}{(x-3)-1} \\ &=\frac{x+2}{x-4} \end{aligned}$

Now, let us equate the denominator equal to zero to determine the domain.

$x-4=0$

$x=4$

Thus, the function becomes undefined at the point $x=4$

Hence, the domain of $(m \circ n)(x)$ is $(-\infty, 4) \cup(4, \infty)$

Now, we shall find the function which has the same domain as $(m \circ n)(x)$

Option A: $h(x)=\frac{x+5}{11}$

The function h(x) has the domain of set of all real numbers $$-\infty$

Thus, the interval $(-\infty,\infty)$ is not the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option A is not the correct answer.

Option B: $h(x)=\frac{11}{x-1}$

Equating the denominator equal to zero, the function becomes undefined at the point $x=1$

Thus, the function h(x) has the domain of $(-\infty,-1) \cup(-1, \infty)$ is not the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option B is not the correct answer.

Option C: $h(x)=\frac{11}{x-4}$

Equating the denominator equal to zero, the function becomes undefined at the point $x=4$

Thus, the function h(x) has the domain of $(-\infty, 4) \cup(4, \infty)$ is the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option C is the correct answer.

Option D: $h(x)=\frac{11}{x-3}$

Equating the denominator equal to zero, the function becomes undefined at the point $x=3$

Thus, the function h(x) has the domain of $(-\infty,3) \cup(3, \infty)$ is not the same domain as $(-\infty, 4) \cup(4, \infty)$

Hence, Option D is not the correct answer.

4 0

3 years ago

What is the solution to the system of equations below? y = one-half x minus 4 and y = negative 2 x minus 9 (–2, –5) (–2, –3) (2,

Maurinko [17]

We have been given a system of equations $y=\frac{1}{2}x-4$ and $y=-2x-9$ . We are asked to find the solution of our given system of equations.

To solve our system of equations, we will equate both equations as:

$\frac{1}{2}x-4=-2x-9$

$\frac{1}{2}x-4+4=-2x-9+4$

$\frac{1}{2}x=-2x-5$

$\frac{1}{2}x+2x=-2x+2x-5$

$\frac{1}{2}x+\frac{4}{2}x=-5$

$\frac{1+4}{2}x=-5$

$\frac{5}{2}x=-5$

$\frac{2}{5}\cdot \frac{5}{2}x=-5\cdot \frac{2}{5}$

$x=-2$

Upon substituting $x=-2$ in equation $y=-2x-9$ , we will get:

$y=-2(-2)-9$

$y=4-9$

$y=-5$

Therefore, the solution of our given system of equations would be $(-2,-5)$ and option A is the correct choice.

7 0

3 years ago

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The vertical change between two points is called___.<br><br>A. up<br>B. down<br>C. run<br>D. rise

morpeh [17]

Answer:

D

Step-by-step explanation:

The term "rise over run" is frequently used when talking about slope. It means the vertical distance over the horizontal distance, so the answer is D, rise.

5 0

3 years ago

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Solve 2x2 + 12x - 14 = 0 by completing the square

vovangra [49]

Answer:

Step-by-step explanation:

$(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\2x^2+12x-14=0\qquad\text{divide both sides by 2}\\\\x^2+6x-7=0\qquad\text{add 7 to both sides}\\\\x^2+2(x)(3)=7\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=7+9\\\\(x+3)^2=16\Rightarrow x+3=\pm\sqrt{16}\\\\x+3=-4\ or\ x+3=4\qquad\text{subtract 3 from both sides}\\\\x=-7\ or\ x=1$

5 0

4 years ago

which ordered pairs are solutions to the inequality y−4x≥−5? Select each correct answer. (−4, 2) (4, 0) (5, −2) (−2, 1) (1, −1)

sukhopar [10]

This graph should help find the coordinates you need that was made of this inequality!

4 0

3 years ago

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