Aprilnietes010idn
Answered

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2. Find the inverse of f(x) = -x3+2.​

Sagot :

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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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