for each function, find an equasion for the inverse. then use composition to verify that the equasion you wrote is the inverse.
f(x)=10x-6
x=10y-6
y=1/10 (x+6)
f(finverse)=f(1/10(x+6))=10(1/10(x+6)-6)
= x+6-6=x
what are the steps?
for each function, find an equasion for the inverse. then use composition to verify that the equasion you wrote is the inverse.
f(x)=10x-6
To find the equation for the inverse of a function, we can follow these steps:
Step 1: Replace f(x) with y.
y = 10x - 6
Step 2: Swap the x and y variables.
x = 10y - 6
Step 3: Solve for y.
x + 6 = 10y
(x + 6)/10 = y
So, the equation for the inverse of f(x) is:
f^(-1)(x) = (x + 6)/10
Now, let's verify that the equation we obtained is indeed the inverse by using composition.
Step 4: Substitute f^(-1)(x) into f(x).
f(f^(-1)(x)) = 10(f^(-1)(x)) - 6
Step 5: Substitute the inverse equation into f(x).
= 10((x + 6)/10) - 6
= x + 6 - 6
= x
Since the final result is equal to x, we've verified that the equation f^(-1)(x) = (x + 6)/10 is the inverse of f(x) = 10x - 6.