Mathematics: 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. ƒ -1(x) = x ƒ -1(4) =

Write the inverse function for the function, ƒ(x)

Ответ:

indiaholmes16

13.03.2022

Mathematics

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

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

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Ответ:

gigi239

25.10.2022

Mathematics

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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. ƒ -1(x) = x ƒ -1(4) =

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