Question

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

Answer 1

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 2

Answer:

$F^{-1}(x)=\frac{1}{9} x$

Step-by-step 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:

$x=\frac{y}{9}$

Step 3:

$y=\frac{x}{9}$

Step 4

$y=f^{-1}(x)=F^{-1}(x)=\frac{x}{9}$

Step 5:

Let:

$a=5$

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

Now:

$F^{-1}(b)=F^{-1}(45)=\frac{45}{9} =5$

Since:

$f(a)=b \rightarrow f^{-1}(b)=a$

We have verified the result.