Restrict the domain of the function f\displaystyle {f} so that the function is one-to-one and has an inverse function. Then find the inverse function f1\displaystyle {f}^{{-{1}}}. Graph f\displaystyle {f}, f1\displaystyle {f}^{{-{1}}}, and the line y=x\displaystyle {y}={x} on the provided graph. State the domains and ranges of both f\displaystyle {f} and f1\displaystyle {f}^{{-{1}}}.


f(x)=(x2)2\displaystyle {f{{\left({x}\right)}}}={\left({x}-{2}\right)}^{{2}} and it's inverse is f1(x)=\displaystyle {{f}^{{-{1}}}{\left({x}\right)}}=  
Graph f(x)\displaystyle {f{{\left({x}\right)}}} using DOTS since you must restrict its domain.

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Clear All Draw: LineParabolaSquare rootDot


f(x)\displaystyle {f{{\left({x}\right)}}}'s domain:   f1(x)\displaystyle {{f}^{{-{1}}}{\left({x}\right)}}'s domain:  
f(x)\displaystyle {f{{\left({x}\right)}}}'s range:   f1(x)\displaystyle {{f}^{{-{1}}}{\left({x}\right)}}'s range: