Answer:
Inverse of F(x)=9x = 1/9x
Step-by-step 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:
[tex]F^{-1}(x)=\frac{1}{9} x[/tex]
Step-by-step explanation:
In order to find the inverse of a function, you can follow the next steps:
Step 1: Write [tex]f(x)=y[/tex]
Step 2: Solve for [tex]x[/tex]
Step 3: Replace every [tex]x[/tex] with a [tex]y[/tex] and replace every [tex]y[/tex] with an [tex]x[/tex]
Step 4: Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]
Step 5: Verify the result by checking that:
[tex]f(a)=b \rightarrow f^{-1}(b)=a[/tex]
Therefore:
Step 1:
[tex]y=9x[/tex]
Step 2:
[tex]x=\frac{y}{9}[/tex]
Step 3:
[tex]y=\frac{x}{9}[/tex]
Step 4
[tex]y=f^{-1}(x)=F^{-1}(x)=\frac{x}{9}[/tex]
Step 5:
Let:
[tex]a=5[/tex]
[tex]F(a)=F(5)=9*5=45\\\\Hence\\\\b=45[/tex]
Now:
[tex]F^{-1}(b)=F^{-1}(45)=\frac{45}{9} =5[/tex]
Since:
[tex]f(a)=b \rightarrow f^{-1}(b)=a[/tex]
We have verified the result.
