Respuesta :

gabby5792

I'll match them for you, but to find the inverse of an equation, all you must do is

  1. Switch x and y
  2. Solve for y again for the "inverse" !

[tex]f(x)^{-1}  = 5x[/tex]  →  [tex]f(x) = \frac{x}{5}[/tex]

[tex]f(x)^{-1} = \frac{x^{3}}{2}[/tex]  →  [tex]f(x) = \sqrt[3]{2x}[/tex]

[tex]f(x)^{-1} = x + 10[/tex]  →  [tex]f(x) = x - 10[/tex]

[tex]f(x)^{-1} = \frac{3(x+17)}{2}[/tex]  →  [tex]f(x) = \frac{2x}{3} -17[/tex]

Hope I help ! :)

kudzordzifrancis

ANSWER

[tex] \boxed {f(x)= \frac{2x}{3} - 17\to \: f ^{ - 1} (x)=\frac{3x + 51}{2}}[/tex]

[tex] \boxed {f(x) = x - 10 \to {f}^{ - 1} (x) = x + 10 }[/tex]

[tex] \boxed {f(x) = \sqrt[3]{2x} \to {f}^{ - 1} (x) = \frac{ {x}^{3} }{2} }[/tex]

[tex] \boxed {f(x) = \frac{x}{5} \to{f}^{ - 1} (x) = 5x}[/tex]

EXPLANATION

1.

Given :

[tex]f(x) = \frac{2x}{3} - 17[/tex]

Let

[tex]y =\frac{2x}{3} - 17[/tex]

Interchange x and y.

[tex]x=\frac{2y}{3} - 17[/tex]

Solve for y.

[tex]x + 17=\frac{2y}{3} [/tex]

[tex]3x + 51=2y[/tex]

[tex]y=\frac{3x + 51}{2} [/tex]

[tex]f ^{ - 1} (x)=\frac{3x + 51}{2} [/tex]

2.

Given: f(x)=x-10

Let y=x-10

Interchange x and y.

x=y-10

Solve for y.

y=x+10

This implies that,

[tex] {f}^{ - 1} (x) = x + 10[/tex]

3.

Given:

[tex]f(x) = \sqrt[3]{2x} [/tex]

Let

[tex]y=\sqrt[3]{2x} [/tex]

Interchange x and y.

[tex]x=\sqrt[3]{2y} [/tex]

solve for y.

[tex] {x}^{3} = 2y[/tex]

[tex]y = \frac{ {x}^{3} }{2} [/tex]

[tex] {f}^{ - 1} (x) = \frac{ {x}^{3} }{2} [/tex]

4.

Given:

[tex]f(x) = \frac{x}{5} [/tex]

Let

[tex]y = \frac{x}{5} [/tex]

Interchange x and y.

[tex]x = \frac{y}{5} [/tex]

Solve for y.

[tex]y = 5x[/tex]

[tex] {f}^{ - 1} (x) = 5x[/tex]

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