A mapping f: A arrow B defined as f(x)=(2 x+3)/(3 x+5), x ∈ A . If f is to be onto, then what are A and B equal to?

Correct answer: D. A=R \ -(5)/(3)\ and B=R \ (2)/(3)\ f(x)=(2 x+3)/(3 x+5) Clearly for domain, 3 x+5 ≠ 0 x ≠-(5)/(3) Domain =A= ℝ - \ -(5)/(3)\ for onto function, Range = Co-domain B= Range of fy=(2 x+3)/(3 x+5)3 x y+5 y=2 x+3 x(3 y-2)=3-5 yx=(3-5 y)/(3 y-2) Clearly, 3 y-2 ≠ 0 y ≠ (2)/(3) B= ℝ - \ (2)/(3)\

NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Functions

NDA 2023 · Mathematics · Functions

A mapping f: A arrow B defined as f(x)=(2 x+3)/(3 x+5), x ∈ A . If...

A mapping

f: A \rightarrow B

defined as

f(x)=\frac{2 x+3}{3 x+5}, x \in A

. If

f

is to be onto, then what are

A

and

B

equal to?

Options

A $A=R \left\{-\frac{5}{3}\right\}$ and $B=R \left\{-\frac{2}{3}\right\}$
B $\mathrm{A}=\mathrm{R}$ and $\mathrm{B}=B=R \left\{-\frac{5}{3}\right\}$
C $A=R \left\{-\frac{3}{2}\right\}$ and $\mathrm{B}=\mathrm{R} \{0\}$
D $A=R \left\{-\frac{5}{3}\right\}$ and $B=R \left\{\frac{2}{3}\right\}$

Correct answer

D. $A=R \left\{-\frac{5}{3}\right\}$ and $B=R \left\{\frac{2}{3}\right\}$

Step-by-step solution

f(x)=\frac{2 x+3}{3 x+5}

Clearly for domain,

3 x+5 \neq 0 \Rightarrow x \neq-\frac{5}{3}\therefore \quad

Domain

=A= \mathbb{R} - \left\{-\frac{5}{3}\right\}\because

for onto function, Range = Co-domain

\Rightarrow B=

Range of

fy=\frac{2 x+3}{3 x+5}3 x y+5 y=2 x+3 \Rightarrow x(3 y-2)=3-5 yx=\frac{3-5 y}{3 y-2}

Clearly,

3 y-2 \neq 0 \Rightarrow y \neq \frac{2}{3}\therefore \quad B= \mathbb{R} - \left\{\frac{2}{3}\right\}

Practice Functions on Quantrex Academy →

More from Functions