Question

Select the correct answer. Which function has an inverse function?

Answer 1

Answer:

The function that has an inverse function is:

            D.  $f(x)=\dfrac{x+3}{7}$

Step-by-step explanation:

We know that " A inverse of a function f(x) exist if it is both 1-1 and onto "

A)

$f(x)=|x-4|+1$

We know that the modulus function is not 1-1.

Since, there are two different 'x' such that the function have the same value.

Take x=1

and take x= 7

In both the cases we have: f(x)=4

Hence, the function does not has a inverse.

B)

$f(x)=25x^2+70x+49$

We know that a  polynomial with even degree is not 1-1.

As it is symmetric about a line x=a

Hence, option: B is incorrect.

C)

$f(x)=x^4$

Again it is a polynomial of even degree.

Hence, it does not has  a inverse.

D)

$f(x)=\dfrac{x+3}{7}$

As the function is both 1-1 and onto.

Hence, the function has a inverse and the inverse function is calculated as:

$f(x)=y\\\\i.e.\\\\\dfrac{x+3}{7}=y\\\\i.e.\\\\x+3=7y\\\\i.e.\\\\x=7y-3$

Hence, the inverse function is:

           $f(y)=7y-3$

              The answer is:

               Option: D