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3 years ago

Please help! I’m in a test rn! If f(x) and g(x) are inverse functions of each other, which of the following statements is true?

Mathematics

1 answer:

White raven [17]3 years ago

5 0

Answer:

D) $(g\cdot f)(x)=x$

Step-by-step explanation:

If two functions $f(x)$ and $g(x)$ are inverse of each other, then the following conditions must be true:

i. $(f\cdot g)(x)=x$

ii. $(g\cdot f)(x)=x$

Therefore, out of the four choices available, only option D matches the condition for inverse function to exist.

Therefore, $(g\cdot f)(x)=x$

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Is 1 = 2 always a false statement?

lutik1710 [3]

Answer:

yes, 1 can never equal 2 unless it is manipulated (ex: 1(2) = 2)

because one is not being manipulated to equal 2 here, it is a false statement and will always be a false statement.

5 0

2 years ago

Read 2 more answers

A recent study of 26 city residents showed that the time they had lived at their present address has a mean of 10.3 years with t

svetlana [45]

Answer:

The 95% confidence interval is $9.15< \mu < 11.45$

Step-by-step explanation:

From the question we are told that

The sample size is n = 26

The mean is $\= x = 10.3$

The standard deviation is $s = 3$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * \frac{3}{\sqrt{26} }$

=> $E = 1.1532$

Generally 95% confidence interval is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $10.3 -1.1532 < \mu < 10.3 + 1.1532$

=> $9.15< \mu < 11.45$

7 0

2 years ago

If you invest $1600 at 5.25% for 18 months, how much simple interest is earned?

Damm [24]

Interest calculator for a $600 investment. How much will my investment of 600 dollars be worth in the future? Just a small amount saved every day, week, or month can add up to a large amount over time. In this calculator, the interest is compounded annually.

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2 years ago

What decimal is equal 35%

iren [92.7K]

Answer:

0.35

Step-by-step explanation:

Divide 35 by 100 and you get 0.35

8 0

3 years ago

Read 2 more answers

A function of the form f(x)=ab^x is modified so that the b value remains the same but the a value is increased by 2. How do the

ANEK [815]

Answer:

The domain and range remain the same.

Step-by-step explanation:

Hi there!

First, we must determine what increasing a by 2 really does to the exponential function.

In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).

Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).

The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.

The range remains the same as well; for the original function, it would have been $y\neq 0$ . Because increasing a by 2 does not move the entire function up or down, the range remains the same.

I hope this helps!

3 0

2 years ago