Question

Given f(x) = the quantity of x minus 1, divided by 2, solve for f−1(5). 2 9 11 15

Answer 1

`f^(-1)(5)=11`

Explanation:

Step 1

Find the inverse function

we have

`f(x)=(x-1)/(2)`

Let

`y=f(x)`

`y=(x-1)/(2)`

Exchanges the variables x for y and y for x

`x=(y-1)/(2)`

Isolate the variable y

`y=2x+1`

Let

`f^(-1)(x)=y`

`f^(-1)(x)=2x+1` ------> inverse function

Step 2

Find
`f^(-1)(5)`

Substitute the value of
`x=5` in the inverse function

`f^(-1)(5)=2(5)+1=11`

Answer 2

f ( x ) = ( x - 1 ) / 2
y = ( x - 1 ) / 2
x - 1 = 2 y
x = 2 y + 1
f ^(-1) ( x ) = 2 x + 1 ( this is inverse function )
f ^(-1) ( 5 ) = 2 * 5 + 1 = 10 + 1 = 11
Answer: C ) 11