How do you find #f^-1(x)# given #f(x)=2x+7#?
2 Answers
Explanation:
Given:
Let y=f(x)
Expressing x in terms of y gives us the inverse of x
Thus,
The
Explanation:
There are a couple of ways to look at function inverses. An inverse of anything allows you to 'undo' whatever you started with. So, if you tie your shoe, it's not there forever - you can always untie it.
We have many inverse functions in math, such as square root is the inverse of squaring a number, etc.
Finding the inverse also reflects the graph across the line y = x.
There are 3 steps to finding an inverse:
1) change notation
So, y = 2x + 7
2) Exchange the x & y variables. Note this is what accomplishes that reflection across the line y = x
So, x = 2y + 7
3) Since x is the dependent variable and y is the independent variable and it is always a zillion times easier to solve a problem in y = form, solve the equation for y.
First subtract 7 from both sides
x - 7 = 2y
Then divide by 2