Please help!! I'll give 30 points and brainliest.

Mathematics

1 answer:

Valentin [98]3 years ago

8 0

Step-by-step explanation:

$3 + \frac{9}{4} = \frac{9}{x+4} \\ \\ \therefore \: \frac{3 \times 4 + 9}{4} = \frac{9}{x+4} \\ \\ \therefore \: \frac{12 + 9}{4} = \frac{9}{x+4} \\ \\ \therefore \: \frac{21}{4} = \frac{9}{x+4} \\ \\ \therefore \:21(x + 4) = 36 \\ \\ \therefore \:21x + 84 = 36\\ \\ \therefore \:21x = 36 - 84\\ \\ \therefore \:21x = - 48\\ \\ \therefore \:x = \frac{-48}{21} \\ \\ \therefore \:x = \frac{-16}{7} \\ \\ \huge \red{ \boxed{ \therefore \:x = - 2 \frac{2}{7} }}\\ \\$

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Step-by-step explanation:

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2 years ago

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

Bingel [31]

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

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