Question

$f:c\to c$ is defined as $f\left(x\right)=\frac{ax+b}{cx+d},bd\ne 0$ then $f$ is a constant function when,

• A. a=c
• B. b=d
• C. ad=bc
• D. ab=cd

Answer 1

Answer: (C)

ad=bc

Solution -

f($x$)=$\frac{ax+b}{cx+d}$ is a constant function,

then lets say it equal to same constant m.

$m(cx+d)=ax+b$

$a=mc$

$b=md$

$\frac{a}{c}$ =$\frac{b}{d}=m$

$\frac{a}{b}$ =$\frac{c}{d}$

$ad=bc$

C is correct.