Can someone help me solve this problem? It’s for a test. Please help!

Match each function with the corresponding restrictions to its domain when p(x)=2x and q(x) = 2^x.

ASHA 777 [7]

Recall that the domain of a function is the set of all x values of the function for which the function is defined.

Given that
$p(x)=2x$ and $q(x)=2^x$

Given that
$r(x)= \frac{q(x)}{p(x)} = \frac{2^x}{2x}$
For the function to be undefined, the denominator should be zero
i.e. 2x = 0 which means that x = 0
Thus, the domain of the function is all real values of x except 0.

Therefore, the restriction is x ≠ 0.

Given that
$r(x)= \frac{1}{p(x)-q(x)} = \frac{1}{2x-2^x}$
For the function to be undefined, the denominator should be zero
i.e.
$2x-2^x=0 \\ 2^x=2x$
For x = 2,
$2^2 = 2(2)=4$
Also, for x = 1
$2^1 = 2(1)=2$
Thus, the domain of the function is all real values of x except 1 and 2.

Therefore, the restriction is x ≠ 1, 2.

Given that
$r(x)= \frac{1}{p(x)+16q(x)}=\frac{1}{2x+16(2^x)}$
For the function to be undefined, the denominator should be zero
i.e.
$2x+16(2^x)=0 \\ 2x+2^4(2^x)=0 \\ 2x+2^{4+x}=0$
For x = -2,
$2(-2)+2^{4-2}=-4+2^2=-4+4=0$ .
Thus, the domain of the function is all real values of x except -2.

Therefore, the restriction is x ≠ -2.

Given that
$r(x)=p(x)\circ q(x)=p(q(x))=2(2^x)$
There is no value of x, for which the function is undefined.
Thus, the domain of the function is all real values of x.

Therefore, there is no restrictions to the domain of the function.

Given that
$r(x)= \frac{q(x)}{p(x)+2}=\frac{2^x}{2x+2}$
For the function to be undefined, the denominator should be zero
i.e.
$2x+2=0 \\ 2x=-2 \\ x = -1$
Thus, the domain of the function is all real values of x except -1.

Therefore, the restriction is x ≠ -1.

6 0

3 years ago

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−62 − (−25)= A) (-87) B) (-37) C) 37 D) 87

vaieri [72.5K]

The answer is B) (-37)

3 0

3 years ago

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Help please lol :)))))))

nasty-shy [4]

How come it’s a right triangle, I think you do a2+b2=C2. Therefore, you do 9.4 times 9.4 and then 15.1 times 15.1. So it will be 9.4 + b2=15.1. 88.36+ b2=228.01. Then you subtract that and it will be 139.65. Then you do square roots because you are trying to get rid of the second power. And the final answer is 11.81736011. How they told you to round it to the nearest tenth, I will be 11.8. I think this is the answer.

6 0

3 years ago

Which price is cheaper? 20% off the original price of $29.99 or 10% off the original price of $26 for a book?

Archy [21]

20% off means that now it costs 80% of original price
80% = 0.8
costs 80% of (means here times (*))original price
29.99*0.8≈23.99

10% off means that now it costs 90% of original price
90%=0.9
costs 90% of (means here times (*))original price
26*0.9=23.40
23.99>23.40,
so is
 10% off the original price of $26 is cheaper

3 0

3 years ago

URGENT Solve -4a + 5 ≤ -7.

Nonamiya [84]

Answer:

a ≥ 3

Step-by-step explanation:

6 0

3 years ago

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