FIND THE INVERSE
[tex]1. \: f(x) = - x3 + 2[/tex]
Substitute Y For F(x).
[tex]2. \: y = - x3 + 2[/tex]
Interchange X And Y.
[tex]3. \: x = - y \times 3 + 2[/tex]
Swap The Sides Of The Equations.
[tex]4. \: - y \times 3 + 2 = x[/tex]
Use The Commutative Property To Reorder The Terms.
[tex]5. \: - 3y + 2 = x[/tex]
Move The Constant To The Right Hand Side And Change Its Sign.
[tex]6. \: - 3y = x - 2[/tex]
Divide. Both Sides Of The Equation By -3.
[tex]7. \: y = - \frac{1}{3} x + \frac{2}{3} [/tex]
Subtitute f-¹(x) Fo Y.
THE ANSWER IS:
[tex]f {}^{ - 1} (x) = - \frac{1}{3} \: x + \frac{2}{3} [/tex]
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