If f (x) = 2x-1/x+5 (x ≠ - 5), then f^{-1} (x) is equal to :

Correct Answer is : 5x+12−x5x+1/2-x2−x5x+1 , x ≠ 2

Correct Answer is : 5x+12−x5x+1/2-x2−x5x+1 , x ≠ 2

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UPSEE Solved Model Paper 7

Question : 119 of 150

Marks: +1, -0

If f (x) =

\frac{2x-1}{x+5}

f^{-1}

(x) is equal to :

Solution:

Given :

f (x) =

\frac{2x-1}{x+5}

(x ≠ - 5)

We have to find

f^{-1}(x)

Let y = f (x) =

\frac{2x-1}{x+5}

⇒ y (x + 5) = 2x - 1

⇒ xy + 5y = 2x - 1

⇒ x (y - 2) = - 1 - 5y

⇒ x =

\frac{-(1+5y)}{-(2-y)}

⇒ x =

\frac{1+5y}{2-y}

∴

f^{-1}

x =

\frac{1+5x}{2-x}

, (x ≠ 2) [Using definition of inverse of function]

Hence, option 'D' is correct.

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