Question

$f:(-\infty ,\infty )\to (-\infty ,\infty )$ is defined by $f\left(x\right)=ax+b;a,b\in R(a\ne 0)$ then $f$ is

• A. injective but not surjective
• B. surjective but not injective
• C. bijective
• D. neither injective nor surjective

Answer 1

Answer: (C)

bijective

$f\left(x\right)=ax+b$
$f^{\prime }\left(x\right)=a$
So $f\left(x\right)$ is increasing if $a>0$ or $f\left(x\right)$ is decreasing if $a<0$.
And $f\left(x\right)$ lies in the interal $(-\infty ,\infty )$ in its domain.
So $f\left(x\right)$ is monotonic & onto, that is, it is bijective