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2 years ago

Find f(x) if g(f(x))=x and g(x)=(x+1)/(x-1)

Mathematics

1 answer:

Firdavs [7]2 years ago

7 0

Answer:

f(x) = (x +1)/(x -1)

Step-by-step explanation:

Let f(x) = y. We want to find y such that ...

g(y) = x

(y +1)/(y -1) = x

y +1 = xy -x . . . . . . multiply by y-1

y -xy = -x -1 . . . . . . add -1 -xy

y(x -1) = x +1 . . . . . . multiply by -1 and factor out y

y = (x +1)/(x -1) . . . . divide by the coefficient of y

Then ...

f(x) = (x +1)/(x -1)

_____

<em>Check</em>

g(f(x)) = ((x +1)/(x -1) +1)/((x +1)/(x -1) -1)

= ((x +1 +x -1)/(x -1)) / ((x +1 -x +1)/(x -1))

= 2x/2

= x

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3 years ago

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HACTEHA [7]

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Option C is the answer.

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To find the equation of the straight line equation i.e, we must be given with the two points $\left (x_{1},y_{1} \right )$ and $\left (x_{2},y_{2}\right )$

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Find f(x) if g(f(x))=x and g(x)=(x+1)/(x-1)​

Find f(x) if g(f(x))=x and g(x)=(x+1)/(x-1)