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MHTCET 13 Apr 2026 Shift 2 Paper

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Question : 119 of 150

Marks: +1, -0

If

g(x)

is the inverse function of

f(x)

f(x)=\frac{5 x+3}{4 x-1}

g(1)=

-4
$\frac{-1}{4}$
$\frac{8}{3}$
$\frac{3}{8}$

Solution:

Concept:

For inverse functions,

g(1)

is the value of

x

for which

f(x)=1

.

Explanation:

We are given

f(x)=\frac{5x+3}{4x-1}

.

To find

g(1)

, set

f(x)=1

.

So,

\frac{5x+3}{4x-1}=1

Multiply both sides by

4x-1

:

5x+3=4x-1

Rearrange the terms:

5x-4x=-1-3

This simplifies to:

x=-4

Hence,

g(1)=-4

.

Answer:

Option A:

-4

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