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

Correct Answer is : 5x+12−x,x≠25 x+1/2-x, x ≠ 22−x5x+1,x=2

Correct Answer is : 5x+12−x,x≠25 x+1/2-x, x ≠ 22−x5x+1,x=2

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MHTCET 20 Apr 2026 Shift 2 Paper

Question : 118 of 150

Marks: +1, -0

f(x)=\frac{2 x-1}{x+5}, x \neq-5

f^{-1}(x)

is equal to

Solution:

Concept:

The inverse of a function is obtained by interchanging

x

and

y

and solving for

y

Explanation:

Let

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

Interchange

x

and

y

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

Multiply both sides by

y+5

x(y+5) = 2y - 1

xy + 5x = 2y - 1

Bring all

y

terms to one side:

xy - 2y = -1 - 5x

Factor out

y

y(x-2) = -(1+5x)

Therefore,

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

So,

f^{-1}(x) = \frac{5x+1}{2-x}

For the inverse to be defined, the denominator must not be zero:

2 - x \neq 0 \Rightarrow x \neq 2

Answer:

Option B:

\frac{5x+1}{2-x},\; x \neq 2

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