Question

Which graph shows a function whose inverse is also a function?

• A.
• B.
• C.
• D.

  

Answer 1

The correct option is A

Explanation for the correct option:

Option(A):

Using the concept of inverse function, it is found that the first graph shows a function whose inverse is also a function.

A function $f\left(x\right)$ will only have an inverse function if: $f\left(a\right)=f\left(b\right)\leftrightarrow a=b$ i.e. is function is one-one, that is, a value of $y$ will have only one respective value of $x$.

In the first graph, for each value of $y$, there is only one value of $x$, so the inverse is also a function, and this is the correct option.

Explanation for the in-correct options:

Option(B):

In the second graph, for example, $x=0$when $y=-1$and when $y=1$, so the inverse is not a function.

Option(C):

In the third graph, for example, $x=-3$ when $y=0$and $y=2,$ so the inverse is not a function.

Option(D):

In the fourth graph, for example, $x=1$ for two values of $y$, so the inverse is not a function.

Therefore only first graph shows a function whose inverse is also a function.

Hence, the correct answer is option (A).