Question

Which function has an inverse function?

Answer 1

F(X)=X^4/7 +27                 .......       

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

A function has an inverse function if and only if it is a one-to-one function. It means for each value of x there exist a unique value of y.

In option 1,

$f(x)=\frac{|x+3}}{5}$

It is an absolute function. For each value of x there axis more than 1 value of f(x). Therefore this function does not has an inverse function.

In option 2,

$F(x)=x^5-3$

The degree of the function is 5 which is an odd number. Therefore it is a one-to-one function. Therefore this function has an inverse function.

In option 3,

$F(x)=\frac{x^4}{7}+27$

The degree of the function is 4 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.

In option 4,

$F(x)=\frac{1}{x^2}$

The degree of the function is 2 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.

Hence option 2 is correct.