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D
Question 4
Using the same algorithm:
• Start with a number and add 2 to it.
• Double the result.
• Subtract 3 from that quantity.
Which function represents the inverse of the above algorithm?

Respuesta :

First find function

[tex]\\ \bull\tt\dashrightarrow f(x)=2(x+3)-3[/tex]

[tex]\\ \bull\tt\dashrightarrow f(x)=2x+6-3[/tex]

[tex]\\ \bull\tt\dashrightarrow f(x)=2x+3[/tex]

Now

[tex]\\ \bull\tt\dashrightarrow y=2x+3[/tex]

[tex]\\ \bull\tt\dashrightarrow x=\dfrac{y-3}{2}[/tex]

But

[tex]\\ \bull\tt\dashrightarrow y=f(x)[/tex]

[tex]\\ \bull\tt\dashrightarrow x=f^{-1}(y)[/tex]

Hence

.

[tex]\\ \bull\tt\dashrightarrow f^{-1}y=\dfrac{y-3}{2}[/tex]

Replace y by x

[tex]\\ \bull\tt\dashrightarrow f^{-1}(x)=\dfrac{x-3}{2}[/tex]

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