Question

Write the inverse function for the function, ƒ(x) = x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.

Answer 1

Hope you'll understand the workings :)

Answer 2

Answer:  The required values are

$f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.$

Step-by-step explanation:  We are given the following function f(x) :

$f(x)=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the values of $f^{-1}(x)$ and $f^{-1}(4).$

Let us consider that

$y=f(x)~~~~~~~~\Rightarrow x=f^{-1}(y).$

So, from equation (i), we get

$f(x)=x+4\\\\\Rightarrow y=f^{-1}(y)+4\\\\\Rightarrow f^{-1}(y)=y-4\\\\\Rightarrow f^{-1}(x)=x-4.$

Substituting x = 4 in the above equation, we get

$f^{-1}(4)=4-4=0\\\\\Rightarrow f^{-1}(4)=0.$

Thus, the required values are

$f^{-1}(x)=x-4~~~~~~~~\textup{and}~~~~~~~~~f^{-1}(4)=0.$