Please help! y=2x
I need to find the inverse, and I am wonderingif the inverse is x= 2y or f-1 = x/2????
if u have the calculator isnt the inverse buttom -1
to find the inverse of a function takes 2 steps
1. interchange the x and y variables
so y = 2x becomes x = 2y
2. Solve this new equation for y
2y = x
y = x/2
so you are correct.
for linear function of the type f(x) = mx + b
it is easy to form the inverse mentally by just "reversing" the steps and operations.
e.g. y = 3x -5
the inverse would be y = (x+5)/3
for the first, after picking any x,
we multiplied by 3 then subtracted 5
for the second, after picking any x,
we added 5 and then divided by 3
notice that not only did we perform the inverse operations, but we also performed those inverse operations in reverse order.
To find the inverse of a function, you can follow these steps:
1. Replace the function notation f(x) with y.
In this case, the function is y = 2x.
2. Swap the x and y variables to solve for the independent variable.
Rewrite the equation as x = 2y.
3. Solve the equation for y.
Divide both sides of the equation by 2 to isolate y:
x/2 = y.
Therefore, the inverse of the function y = 2x is x/2. So, f^(-1)(x) = x/2.
To confirm this, you can also switch back the variables to verify:
- Starting with the original function: y = 2x
- Swapping variables: x = 2y
- Solving for y: y = x/2
Hence, the inverse function is indeed f^(-1)(x) = x/2.