Question

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?

Answer 1

First find function

`\\ \bull\tt\dashrightarrow f(x)=2(x+3)-3`

`\\ \bull\tt\dashrightarrow f(x)=2x+6-3`

`\\ \bull\tt\dashrightarrow f(x)=2x+3`

Now

`\\ \bull\tt\dashrightarrow y=2x+3`

`\\ \bull\tt\dashrightarrow x=(y-3)/(2)`

But

`\\ \bull\tt\dashrightarrow y=f(x)`

`\\ \bull\tt\dashrightarrow x=f^(-1)(y)`

Hence

.

`\\ \bull\tt\dashrightarrow f^(-1)y=(y-3)/(2)`

Replace y by x

`\\ \bull\tt\dashrightarrow f^(-1)(x)=(x-3)/(2)`