Find the Inverse f(x)=1+ square root of 1+x

Problem

ƒ(x)=1+√(,1+x)

Solution

1. Replace ƒ(x) with y to set up the equation for the inverse.

y=1+√(,1+x)

2. Swap the variables x and y to begin solving for the inverse function.

x=1+√(,1+y)

3. Isolate the radical term by subtracting 1 from both sides of the equation.

x−1=√(,1+y)

4. Square both sides of the equation to eliminate the square root.

(x−1)2=1+y

5. Solve for y by subtracting 1 from both sides.

y=(x−1)2−1

6. Define the domain of the inverse function based on the range of the original function ƒ(x) which is x≥1

ƒ(x)(−1)=(x−1)2−1

Final Answer

ƒ(x)(−1)=(x−1)2−1,x≥1

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