What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)?

Which of these statements is true for f(x)=(1/10)^x

lana66690 [7]

Step-by-step explanation:

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Analyzing option A)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Putting $x = 1$ in the function

$f\left(1\right)=\:\left(\frac{1}{10}\right)^1$

$f\left(1\right)=\:\left\frac{1}{10}\right$

So, it is TRUE that when $x = 1$ then the out put will be $f\left(1\right)=\:\left\frac{1}{10}\right$

Therefore, the statement that '' The graph contains $\left(1,\:\frac{1}{10}\right)$ '' is TRUE.

Analyzing option B)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The range of the function is the set of values of the dependent variable for which a function is defined.

$\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k$

$k=0$

$f\left(x\right)>0$

Thus,

$\mathrm{Range\:of\:}\left(\frac{1}{10}\right)^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}$

Therefore, the statement that ''The range of $f(x)$ is $y > \frac{1}{10}$ " is FALSE

Analyzing option C)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The domain of the function is the set of input values which the function is real and defined.

As the function has no undefined points nor domain constraints.

So, the domain is $-\infty \:$

Thus,

$\mathrm{Domain\:of\:}\:\left(\frac{1}{10}\right)^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Therefore, the statement that ''The domain of $f(x)$ is $x>0$ '' is FALSE.

Analyzing option D)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

As the base of the exponential function is less then 1.

i.e. 0 < b < 1

Thus, the function is decreasing

Also check the graph of the function below, which shows that the function is decreasing.

Therefore, the statement '' It is always increasing '' is FALSE.

Keywords: function, exponential function, increasing function, decreasing function, domain, range

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3 years ago

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Explain how to find 4 times 754 using two different methods

Nina [5.8K]

1. 4x754=5278
2. you could use exponets

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3 years ago

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Solve 7x-2y=11 for y

Leni [432]

Answer:

y = 7/2x -11/2

Step-by-step explanation:

7x-2y=11

Subtract 7x from each side

7x-2y -7x = -7x+11

-2y = -7x+11

Divide each side by -2

-2y/-2 = -7x/-2 +11/-2

y = 7/2x -11/2

8 0

2 years ago

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Whats the simplified ratio if 4 : 22 : 30

masya89 [10]

On dividing all the three ratios with 2 u can simplify it as

2:11:15

Hope it helps.
Dont forget to say thx if it helps

6 0

3 years ago

Is (-3, 1) a solution to this system of inequalities?

Maksim231197 [3]

Answer:

No

Step-by-step explanation:

5(-3)= -15

5(1)= 5

-15+5=-10

-10 is greater than -19 not less than or equal too.

Hope this helps!

5 0

2 years ago