Question

f-exists if fis a. one to one b. surjective c. bijective d. into O a Ob С d​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\sf{ {f}^{ - 1} }$ exists if f is

a. one to one

b. surjective

c. bijective

d. into

EVALUATION

Here the given function is f

We are aware of the Theorem that a function f is invertible if and only if f is bijective

So if f is bijective then $\sf{ {f}^{ - 1} }$ exists

Let us explain it by an example

Let us consider a function f(x) = x + 1

Clearly f is bijective

So f is invertible

Thus $\sf{ {f}^{ - 1} }$ exists

Now

$\sf{ {f}^{ - 1}(x) = x - 1 }$

FINAL ANSWER

Hence the correct option is c. bijective

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