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mihalych1998 [28]
3 years ago
15

Find the inverse function of f(x) = x+2/x+1

Mathematics
2 answers:
lesya692 [45]3 years ago
6 0

Answer:

f^{-1}(x) = \frac{2-x}{x-1}

Step-by-step explanation:

Let y = f(x) and rearrange making x the subject

y = \frac{x+2}{x+1} ( multiply both sides by (x + 1)

y(x + 1) = x + 2 ← distribute left side

yx + y = x + 2 ( subtract x from both sides )

yx - x + y = 2 ( subtract y from both sides )

yx - x = 2 - y ← factor out x on the left side

x(y - 1) = 2 - y ← divide both sides by (y - 1 )

x = \frac{2-y}{y-1}

Change y back into terms of x, thus

f^{-1}(x) = \frac{2-x}{x-1}

madam [21]3 years ago
5 0

Answer:   \bold{f^{-1}(x)=\dfrac{2-x}{x-1}\qquad \implies \qquad f^{-1}(x)=-\dfrac{x-2}{x-1}}

<u>Step-by-step explanation:</u>

Inverse is when you swap the x's and y's and solve for y.  <em>f(x) is y.</em>

y=\dfrac{x+2}{x+1}\\\\\\\\\underline{\text{Swap the x's and y's}}\\\\x=\dfrac{y+2}{y+1}\\\\\\\\\underline{\text{solve for y}}\\\\x(y+1)=y+2\\\\xy+x=y+2\qquad \qquad \text{distributed x into y+1}\\\\xy-y=2-x\qquad \qquad \text{subtracted x and y from both sides}\\\\y(x-1)=2-x\qquad \qquad \text{factored out y on the left side}\\\\\\y=\dfrac{2-x}{x-1}}\qquad \qquad \text{divided both sides by x-1}

\large\boxed{f^{-1}(x)=\dfrac{2-x}{x-1}}

This is equal to: f^{-1}(x)=-\dfrac{x-2}{x-1}

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Step-by-step explanation:

4 0
3 years ago
What is x? <br><br> Thank you
zepelin [54]

Answer:

None of those answers are correct

Step-by-step explanation:

There are no real solutions

Let's solve your equation step-by-step.

2+2x−3

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=

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Step 1: Cross-multiply.

2+2x−3

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(2+2x−3)*(x+2)=(3x+4)*(2x+3)

2x2+3x−2=6x2+17x+12

Step 2: Subtract 6x^2+17x+12 from both sides.

2x2+3x−2−(6x2+17x+12)=6x2+17x+12−(6x2+17x+12)

−4x2−14x−14=0

For this equation: a=-4, b=-14, c=-14

−4x2+−14x+−14=0

Step 3: Use quadratic formula with a=-4, b=-14, c=-14.

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−b±√b2−4ac

2a

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2(−4)

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8 0
3 years ago
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What is an equation of the line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ?
Elza [17]

Answer:

y=-2x-3

Step-by-step explanation:

Since our equation is in standard form Ax+By=C we must first manipulate the equation so that we have it in the slope-intercept form such that y=mx+b.  Therefore:

-x+2y=4\\2y=x+4\\\\y=\frac{x+4}{2}\\\\y=\frac{1}{2}x+2

Therefore, our slope is 1/2 and our y-intercept is 2.  Now in order to determine a perpendicular line to the one stated above we must then get the negative inverse of our slope meaning \frac{1}{2}=-2 (negative reciprocal).  Now we must use the point slope formula:

y=m(x-x_1)+y_1

Where m is the slope, x1 is -2 and y1 is 1 (because of the ordered pair given). And so:

y=-2(x-(-2))+1\\\\y=-2(x+2)+1\\\\y=-2x-4+1\\\\y=-2x-3

Therefore, the line that is perpendicular to -x+2y=4 is y=-2x-3.


6 0
3 years ago
If the graph of y = 72 + 6 is translated 4 units down, which equation describes the new graph?
matrenka [14]

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6 0
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jarptica [38.1K]

Answer:

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3 0
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