Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Let A , B , and C be subsets of real numbers. Let f : A → B and g: B → C be two functions such that gof is onto. the which of the following is true

Options:

f and g both are necessarily onto

f is necessarily onto

f need not be onto

None of these

Correct Answer:

f need not be onto

Explanation:

$g(f(x))$ → onto ⇒ for every $g(f(x))$

there exists atleast one $f(x)$

but $f(x)$ ⇒ there exist atleast one $x$ so $f(x)$ is not necessarily onto