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Goryan [66]
3 years ago
15

What is the inverse function of f(x)= x/x-2?​

Mathematics
1 answer:
jarptica [38.1K]3 years ago
5 0

Answer:

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

Step-by-step explanation:

Start by replacing f(x) by the variable "y" and solving for x in the equation:

f(x)=\frac{x}{x-2} \\y=\frac{x}{x-2}\\(x-2)\,y=x\\xy-2y=x\\xy-x=2y\\x(y-1)=2y\\x=\frac{2y}{y-1}

Now do the final replacement using the inverse function notation, and replacing "y" with "x":

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

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Vedmedyk [2.9K]
2cosx=2sin2x. Sin2x is an identity for 2sinxcos. So 2[2sinxcosx] gives you 4sinxcosx. 2cosx=4sinxcosx. Divide 2cosx on both sides and gives you 2sinx=0 and divide again, sinx=0. Sinx is 0 at 0 and 360 degrees, or pi and 2pi. So thats what x would be. 0,360,pi,2pi.
4 0
3 years ago
Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
Diano4ka-milaya [45]
Foil method:
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8

Distributive property:

(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8

Both methods are efficient, it all depends with the users preference
7 0
3 years ago
Mr. Strand washed 2 - 5 of his laundry. His son washed 1 - 4 of it. Who washed most of the laundry? How much of the laundry stil
fredd [130]

Answer:

His son did.

Step-by-step explanation:

His son: 1/4 = 25%

Mr. Strand: 2/5 = 20%

They also need 55% more to wash or in other words 11/20.

7 0
3 years ago
Use the above diagram to solve for y. You will NEED to show and discuss the similar triangles in the diagram. You will need to s
olganol [36]
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8 0
3 years ago
-9x - 3y = 6 find the value of y when x equals -2
belka [17]

Answer:

y=4

Step-by-step explanation:

-9x-3y=6\\18-3y=6\\-3y=-12\\y=4

4 0
3 years ago
Read 2 more answers
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