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For the function f(x) = √x/2, find f-1(x).

Sagot :

[tex]\begin{gathered} f(x)=\frac{\sqrt[]{x}}{2} \\ \end{gathered}[/tex]

1. replace f(x) with y:

[tex]\begin{gathered} y=\frac{\sqrt[]{x}}{2} \\ \end{gathered}[/tex]

2. Replace every x with a y and replace every y with an x:

[tex]\begin{gathered} x=\frac{\sqrt[]{y}}{2} \\ \end{gathered}[/tex]

3. Solve for y:

[tex]y=4x^2=(2x)^2[/tex]

4. replace y with f-1(x):

[tex]f^{-1}(x)=(2x)^2[/tex]

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