true or false? the function f-1 (x)-x/9 is the inverse function of f(x)=9x
Use the inverse test:
If g(x) is the inverse of f(x), then
f(g(x))=x
Try it:
Let g(x)=x/9
f(x)=9x
f(g(x))=f(x/9)=9(x/9)=x
What is your conclusion?
To determine whether the function f-1(x) = x/9 is the inverse function of f(x) = 9x, we need to follow a few steps.
Step 1: Start with the original function f(x) = 9x.
Step 2: Replace f(x) with y.
So, we have the equation y = 9x.
Step 3: Swap x and y.
Now, we need to interchange the roles of x and y. This gives us x = 9y.
Step 4: Solve for y.
To find the inverse function, we need to solve the equation for y.
Start with the equation x = 9y and isolate y by dividing both sides of the equation by 9:
x/9 = y.
Step 5: Replace y with f-1(x).
We now have the equation f-1(x) = x/9.
Therefore, the inverse function of f(x) = 9x is f-1(x) = x/9.
So, the statement is true.