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3 years ago

What is the domain of f(x)=3^x

Mathematics

1 answer:

julsineya [31]3 years ago

8 0

Answer:

The domain of the function is $D=(-\infty,\infty,x|x\in \mathbb R)$

Step-by-step explanation:

Given : Function $f(x)=3^x$

To find : What is the domain of the function given?

Solution :

Domain is defined as the set of values in which function is defined.

Since, The given function is an exponential function.

In this case there is no real numbers that makes the expression undefined.

i.e. Domain of the given function is from -infinity to +infinity

or $D=(-\infty,\infty,x|x\in \mathbb R)$

Therefore, The domain of the function is $D=(-\infty,\infty,x|x\in \mathbb R)$

You might be interested in

Which of the following functions could be f(x) ?

notka56 [123]

Answer:

B. f(x) = -x^3 - x^2 + 7x - 4

Step-by-step explanation:

For this problem, we want to find the fastest-growing term in our given expressions and equate them when x is - infinite and when x is infinite to see the given trends.

For each of these equations, we will simply take the terms with the highest power and consider those. The two cases we need to consider is + infinite for x and - infinite for x. Let's check each of these equations.

Note, any value raised to an even power will be positive. Any negative value raised to an odd power will be negative.

[A] - x^4

When x is +∞ --> - (∞)^4 --> f(x) is -∞

When x is -∞ --> - (-∞)^4 --> f(x) is -∞

[B] - x^3

When x is +∞ --> - (∞)^3 --> f(x) is -∞

When x is -∞ --> - (-∞)^3 --> f(x) is ∞

[C] 2x^5

When x is +∞ --> 2(∞)^5 --> f(x) is ∞

When x is -∞ --> 2(-∞)^5 --> f(x) is -∞

[D] x^4

When x is +∞ --> (∞)^4 --> f(x) is ∞

When x is -∞ --> (-∞)^4 --> f(x) is ∞

Notice how only option B, when looking at asymptotic (fastest-growing) values, satisfies the originally given conditions for the relation of x to f(x).

Cheers.

8 0

3 years ago

Benny is trying to learn how to ride a bike, but is terrified of falling. He did some research, and discovered that if he rides

Anestetic [448]

Answer:

a) 7.14% probability that Benny was learning to ride a bike using the training wheels

b) 28% probability that Benny was learning to ride a bike using the training wheels

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.

a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that Benny was using each of these 3 methods is equal

This means that $P(B) = \frac{1}{3}$

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that $P(A|B) = 0.1$

Probability of falling:

1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

$P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667$

$P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714$

7.14% probability that Benny was learning to ride a bike using the training wheels

b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?

Similar as above, just some probabilities change.

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that he was using training wheels is 0.7

This means that $P(B) = 0.7$

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that $P(A|B) = 0.1$

Probability of falling:

0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

$P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25$

$P(B|A) = \frac{0.7*0.1}{0.25} = 0.28$

28% probability that Benny was learning to ride a bike using the training wheels

7 0

3 years ago

125m into mm (1m = 1000mm) With complete process pls

tino4ka555 [31]

Answer:

125000mm

explanation

solution:

here,

1m=1000mm

now,

125m= 125×1000

= 125000

hence, 125m= 125000mm

6 0

2 years ago

Which solid has a greater volume?

vivado [14]

Answer:

Step-by-step explanation:

When you find the volume for the cone and cylinder they are both 235.62

6 0

3 years ago

Harriet earns the same amount of money each day. Her gross pay at the end of 7 work days is 35h + 56 dollars. Which expression r

Alex_Xolod [135]

Answer:

Gross pay per days is 5h+8 dollars

Step-by-step explanation:

we are given

total gross pay =35h+56 dollars

total number of days =7

we know that

gross pay per day = ( total gross pay)/(total number of days)

we can plug values

gross pay per day is

$=\frac{35h+56}{7}$

we can simplify it

$=\frac{7(5h+8)}{7}$

$=5h+8$

7 0

3 years ago

Read 2 more answers