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FrozenT [24]
2 years ago
11

If f(x)=sinx 2x 1 and g is the inverse function of f

Mathematics
1 answer:
Bingel [31]2 years ago
8 0

The value of the derivative of the function g(x) at x = 1 will be 1/3. Then the correct option is A.

<h3>What is an inverse function?</h3>

A function that may convert into another function is known as an inverse function or anti-function.

If the function is f(x) = sinx + 2x + 1.

Then the derivative of an inverse function g(x) of a function f(x) at a given value (a) will be

\rm g'(a) = \dfrac{1}{f'(g(a))}

The derivative of f(x) will be

f'(x) = cos x + 2

Then the given value of a will be

a = 1

g(x) = f⁻¹(x)

put x = 0, then we have

f(0) = sin 0 + 2(0) + 1

f(0) = 1

Put x = 1, in the function f⁻¹(x). Then we have

f⁻¹(1) = 0

and

g(1) = 0

Then put a = 1, then we have

\rm g'(a) = \dfrac{1}{f'(g(a))}\\\\g'(1) = \dfrac{1}{f'(g(1))}\\\\g'(1) = \dfrac{1}{f'(0)}\\\\g'(1) = \dfrac{1}{\cos 0 + 2}\\\\g'(1) = \dfrac{1}{1+2}= \dfrac{1}{3}

More about the inverse function link is given below.

brainly.com/question/2541698

#SPJ4

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Look at the Schoology problem provided below.
lys-0071 [83]

Answer:

k = 4 units

Step-by-step explanation:

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

k² + 7.5² = 8.5²

k² + 56.25 = 72.25 ( subtract 56.25 from both sides )

k² = 16 ( take the square root of both sides )

k = \sqrt{16} = 4

6 0
3 years ago
Read 2 more answers
An elevator has a placard stating that the maximum capacity is 1296 lb long dash — 8 passengers.​ So, 8 adult male passengers ca
Masja [62]

Answer:

There is a 98.26% probability that it is overloaded.

This elevator does not appear to be safe.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by

Z = \frac{X - \mu}{\sigma}

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

Assume that weights of males are normally distributed with a mean of 170 lb, so \mu = 170

They have a standard deviation of standard deviation of 29 lb, so \sigma = 29.

We have a sample of 8 adults, so we have to find the standard deviation of the sample to use in the place of \sigma in the Z score formula.

s = \frac{\sigma}{8} = \frac{29}{8} = 3.625

Find the probability that it is overloaded because they have a mean weight greater than 162 lb, so X = 162

Z = \frac{X - \mu}{\sigma}

Z = \frac{162 - 170}{3.625}

Z = -2.21

Z = -2.21 has a pvalue 0.0174.

So, there is a 1-0.0174 = 0.9826 = 98.26% probability that it is overloaded.

Any probability that is above 95% is considerer unusually high. So, this elevator does not appear to be safe, since there is a 98.26% probability that it is overloaded.

8 0
3 years ago
The length of a parallelogram exceeds its breadth by 30 cm. If the perimeter of the parallelogram is 2 m 60 cm, find the length
Nuetrik [128]

\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}

\longrightarrow \sf{2(1 + b) = 260}

\longrightarrow \sf{2(x+30+x) = 260}

\longrightarrow \sf{ 2x+30 = \dfrac{260}{20} }

\longrightarrow \sf{2x + 30 =130}

\longrightarrow \sf{2x = 130 - 30}

\longrightarrow \sf{2x = 100}

\longrightarrow \sf{x=  \dfrac{100}{2} }

• \longrightarrow \sf{b= \underline{50cm}}

\longrightarrow \sf{= x + 30}

\longrightarrow \sf{= 50 + 30}

• \longrightarrow \sf{ \underline{80cm}}

\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}

\large\bm{Breadth= \: 50cm}

\large\bm{Length= \: 80cm}

3 0
2 years ago
If h(x)=(fog)(x) and h(x) = sqrt x+5, find g(x) if f(x) = sqrtx+2
Katen [24]

Answer: The value of g(x) is x+3.

Step-by-step explanation:

Since we have given that

h(x)=f\circ g(x)

Here,

h(x)=\sqrt{x+5}\\\\and\\\\f(x)=\sqrt{x+2}

We need to find the value of g(x):

f(x)=\sqrt{x+2}\\\\f(g(x))=\sqrt{g(x)+2}\\\\h(x)=\sqrt{g(x)+2}\\\\\sqrt{x+5}=\sqrt{g(x)+2}\\\\x+5=g(x)+2\\\\g(x)=x+5-2=x+3

Hence, the value of g(x) is x+3.

3 0
3 years ago
Unit Test
Virty [35]
I believe it’s b because of the way that it is
6 0
3 years ago
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