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Savatey [412]
3 years ago
14

For the funtion f(x)= (x+7)^5, Find f^-1 (x)

Mathematics
1 answer:
quester [9]3 years ago
6 0

Answer:

The inverse of function f(x)= (x+7)^5 is \mathbf{f^{-1} (x)=\sqrt[5]{x}+7}

Option A is correct option.

Step-by-step explanation:

For the function f(x)= (x+7)^5, Find f^{-1} (x)

For finding inverse of x,

First let:

y=(x+7)^5

Now replace x with y and y with x

x=(y+7)^5

Now, solve for y

Taking 5th square root on both sides

\sqrt[5]{x}=\sqrt[5]{(y+7)^5}\\\sqrt[5]{x}=y+7\\=> y+7=\sqrt[5]{x}\\y=\sqrt[5]{x}-7

Now, replace y with f^{-1} (x)

f^{-1} (x)=\sqrt[5]{x}+7

So, the inverse of function f(x)= (x+7)^5 is \mathbf{f^{-1} (x)=\sqrt[5]{x}+7}

Option A is correct option.

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AleksAgata [21]

Answer:

y=3

Step-by-step explanation:

it says that y is the inverse of x so if x=3 and y=8, so if x=8 than y must equal 3

3 0
3 years ago
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Find an equation of the tangent line to the hyperbola: x^2/a^2 - y^2/b^2 = 1 at the point (x0,x1)
musickatia [10]

The standard form of a hyperbola is <span><span><span>x2/</span><span>a2 </span></span>− y<span><span>2/ </span><span>b2 = 1
the tangent line is the first derivative of the function</span></span></span><span>y′ = <span>b^2x/ a^2 y
hence the slope is </span></span><span>m = <span>b^2 x0 / <span>a^2 <span>x1

</span></span></span></span>Therefore the equation of the tangent line isy−x1 = b^2 x0 / a^2 x1* (x−x0)

8 0
3 years ago
What is an equation of the line that passes through the points (4,-5) and (-2,7)
Korvikt [17]

Answer:

y = -2x + 3

Step-by-step explanation:

y2 - y1/ x2 - x1

7 - (-5) / -2 - 4

-2

The slope is -2.

To find the y-intercept, you need to plug the coordinates into the equation.

y = -2x + b

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5 0
2 years ago
Can someone help me with this. Will Mark brainliest.
Mkey [24]

Answer:

no.

Step-by-step explanation:

since 2 of the sides are much longer than the shorter sides, diagonals of a rectangle will not intersect at a right angle (perpendicular) whereas a square, with all sides equal, would. This is because the distance from the center to each of the corners is the same for each corner.

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3 years ago
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slega [8]

Answer:

Option 2, 3, 4

Step-by-step explanation:

It cannot be the 1st option because a linear function doesn't have an x^{2} and adding an x to an x will not make it squared. ax + by = c is the linear equation.

It can be the 2nd option because the quadratic formula is  f(x) = ax^{2} + bx + c and the middle portion could cancel when adding 2 together.

It can be option 3, because f(x) = ax^{2} + bx + c plus ax + by = c could give you the resulting function f(x) = -3x^{2} +5

It can be option 4 because multiplying ax + by = c by ax + by = c would give you an x^{2}.

It cannot be option 5 because ax^{2} + bx + c multiplied by ax^{2} + bx + c would give you a function with x^{4}

8 0
3 years ago
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