Question

If F(x)=9x which of the following is the inverse of F(x)

Answer 1

Inverse of F(x)=9x = 1/9x

Explanation:

If F(x)=9x

which of the following is the inverse of F(x)

When talking about inverse of a function, we are talking about reversal. Therefore, an inverse function is the inverse of another function. In order to get the inverse of a particular function, we reverse the denominator to become the numerator and the numerator to become the denominator.

So for the function,

F(x)=9x, the numerator is 9x and the denominator is 1

Reversing the numerator and denominator, .

Inverse of F(x)=9x = 1/9x

Answer 2

`F^(-1)(x)=(1)/(9) x`

Explanation:

In order to find the inverse of a function, you can follow the next steps:

Step 1: Write
`f(x)=y`

Step 2: Solve for
`x`

Step 3: Replace every
`x` with a
`y` and replace every
`y` with an
`x`

Step 4: Replace
`y` with
`f^(-1)(x)`

Step 5: Verify the result by checking that:

`f(a)=b \rightarrow f^(-1)(b)=a`

Therefore:

Step 1:

`y=9x`

Step 2:

`x=(y)/(9)`

Step 3:

`y=(x)/(9)`

Step 4

`y=f^(-1)(x)=F^(-1)(x)=(x)/(9)`

Step 5:

Let:

`a=5`

`F(a)=F(5)=9*5=45\\\\Hence\\\\b=45`

Now:

`F^(-1)(b)=F^(-1)(45)=(45)/(9) =5`

Since:

`f(a)=b \rightarrow f^(-1)(b)=a`

We have verified the result.