Math

QuestionFind the inverse function f1(x)\mathrm{f}^{-1}(\mathrm{x}) for f(x)=x+4f(x)=x+4. What is f1(x)=?f^{-1}(x)=?

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x+4f(x) = x +4 . We need to find the inverse of this function, denoted as f1(x)f^{-1}(x)

STEP 2

The general method to find the inverse of a function f(x)f(x) is to switch xx and yy and then solve for yy.So, we start with the equation y=f(x)y = f(x), which in this case is y=x+4y = x +4.

STEP 3

Switch xx and yy to get x=y+x = y +.

STEP 4

Now, solve for yy to get the inverse function.Subtract4 from both sides of the equation to isolate yy.
y=x4y = x -4

STEP 5

Finally, we write the inverse function as f1(x)=x4f^{-1}(x) = x -4.
So, the inverse of the function f(x)=x+4f(x) = x +4 is f1(x)=x4f^{-1}(x) = x -4.

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