If a function f: R-\ l\ arrow R-\ m\ defined by f(x)=(x+3)/(x-2) is a bijection, then 3 l+2 m=

Correct answer: C. 8 f(x)=(x+3)/(x-2) f(x) is not defined for x=2 i.e. domain of f(x) is R-\ 2\ l=2 Now, y=(x+3)/(x-2)x y-2 y=x+3x(y-1)=2 y+3x=(2 y+3)/(y-1)y can take any value except y=1 Co-domain =R-\ 1\ m=13 l+2 m=3(2)+2(1)=8

BITSAT 2024Paper 1

Exam: BITSAT
Year: 2024
Paper: Paper 1
Subject: Mathematics
Chapter: Functions

BITSAT 2024 · Paper 1 · Mathematics · Functions

If a function f: R-\ l\ arrow R-\ m\ defined by f(x)=(x+3)/(x-2) is...

If a function

\mathbf{f}: \mathbf{R}-\{l\} \rightarrow \mathbf{R}-\{m\}

defined by

f(x)=\frac{x+3}{x-2}

is a bijection, then

3 l+2 m=

Options

A $10$
B $12$
C $8$
D $14$

Correct answer

C. $8$

Step-by-step solution

f(x)=\frac{x+3}{x-2}\because \quad f(x)

is not defined for

x=2

i.e. domain of

f(x)

\mathrm{R}-\{2\}\therefore l=2

Now,

y=\frac{x+3}{x-2}x y-2 y=x+3x(y-1)=2 y+3x=\frac{2 y+3}{y-1}y

can take any value except

y=1

Co-domain

=\mathrm{R}-\{1\}m=13 l+2 m=3(2)+2(1)=8

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