SOLUTION: Find the inverse function of f(x) = √(x+2)+2

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Question 1199856: Find the inverse function of f(x) = √(x+2)+2
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer:
Domain of inverse:
Range of inverse:
The graph is shown below.

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Work Shown:
















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Explanation:
Replace f(x) with y. Swap x and y as shown in step 3. Then solve for y to determine the inverse.

The domain of f(x) is which is to avoid a negative value under the square root.
This means the range of the inverse is
The domain and range swap roles when going from original function to inverse, and vice versa, simply because of the swap of x and y mentioned earlier.

The range of f(x) is
This means the domain of the inverse is

Graph:

The original f(x) function is in green.
The inverse function is in blue.
To go from the green curve to the blue curve, and vice versa, reflect over the dashed line y = x.

Note that the inverse is a half-parabola since it is only drawn when (domain of the inverse).

Graphing tools such as Desmos and GeoGebra are very useful as quick visual verification methods.
Answer by ikleyn(52865)   (Show Source): You can put this solution on YOUR website!
.
Find the inverse function of f(x) = √(x+2)+2
~~~~~~~~~~~~~~~ 

The given function is 

    f(x) = .


In wording form, it  " adds 2 to x;  then takes the square root;  then adds 2, again ".


The inverse function  f^-1(x)  makes the opposite operations in reverse order. 


In other words,  f^-1(x)  makes the following:


    it subract 2 from the argument; then raise to degree 2; then subtract 2:

        f^-1(x) = .    ANSWER

Solved.


The answer is the same as in the post by other tutor;
but the method is different.

Having two different methods of solution, you may use
either method to get the answer, and then use another method for checking.



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