Question

$f:Q\to Q$ is defined by $f(x)=15x+7$ is

• A. injective only
• B. surjective only
• C. bijective
• D. neither injective nor surjective

Answer 1

Answer: (C)

$f(x_1)=f(x_2)\Rightarrow x_1=x_2\to f$ is one-one
Let $f(x)=y\Rightarrow 15x+7=y\Rightarrow x=\frac{y-7}{15}\in Q$
$\forall y\in Q\Rightarrow f$ is onto