finding the inverse of a function?

Question

i hate funtions as is, but this inverse stuff is nuts, somthing about replacing the x's with the y's, and i dunno... help would be greatly appreciated. really basic, drawn out, dumbed down help.

Answer 1

Find Inverse Function (1) - Tutorial
Examples on how to find inverse functions analytically are presented. Detailed solutions are also included. If you wish to first review the definition and some properties of the inverse function Go Here.




Example 1: Find the inverse function of f given by



f(x) = 2x + 3
Solution to example 1:
write the function as an equation.
y = 2x + 3


solve for x.
x = (y - 3)/2


now write f-1(y) as follows .
f -1(y) = (y - 3)/2
or
or f -1(x) = (x - 3)/2


Check
f(f -1(x))=2(f -1(x)) + 3


=2((x-3)/2)+3

=(x-3)+3

=x


f -1(f(x))=f -1(2x+3)


=((2x+3)-3)/2

=2x/2

=x

conclusion: The inverse of function f given above is f -1(x) = (x - 3)/2

Matched Exercise 1: Find the inverse function of f given by



f(x) = -x - 4

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Example 2: Find the inverse function of f given by

f(x) = (x - 3)2, if x >= 3
Solution to example 2:

write the function as an equation.

y = (x - 3)2



solve for x, two solutions .

x = 3 + sqrt(y)


x = 3 - sqrt(y)


the first solution is selected since x >= 3, write f-1(y) as follows.


f -1(y) = 3 + sqrt(y)


or


f -1(x) = 3 + sqrt(x)


Check

f(f -1(x))=((3+sqrt(x))-3)2


=(sqrt(x))2


=x


f -1(f(x))=3+sqrt((x-3)2)


=3+|x-3| (since x >= 3, x-3 >= 0, |x-3| = x-3)


=3+(x-3)


=x

conclusion:
The inverse of function f given above is f -1(x) = 3 + sqrt(x)

Matched Exercise 2: Find the inverse function of f given by

f(x) = (x + 1)2, if x >= -1
More links and references related to the inverse functions.

Answer 2

Ok. Unlike the other long and seemingly complicated posts, I'll do a quick and simple one.

A function takes the form of f(x) = y or y = x + 3.

In the case of y = x + 3, "y" is the subject of the function.

To obtain the inverse of a function, MAKE "X" the SUBJECT instead of "y". Thus, you are going to make the equation begin like this: x = ...

So in this case,
y = x + 3, Bringing 3 over,
x = y - 3

"x" is now the subject of the equation in x = y - 3. Now write "x" as "y^(-1)" and write "y" as "x". After this substitution you should have:

y^(-1) = x - 3

This is the inverse of the original eqaution.

Hope this helps.

PS: "y^(-1)" means the inverse of "y". The superscript "-1" means inverse.

Answer 3

Inverse functions are like you just said. You swap the y's and the x's. For example:

x+3=y

The inverse for this function is y+3=x; then you solve for y to get y=x-3

Answer 4

if you have to find the inverse of f(x)= (x+2)/4
than all u have to do is equate it with f(x)= y
x=f(inverse)y

(x+2)/4=y
(x+2)=4y
x=4y-2
hence the inverse of f(x) is by replacing y with x in the final answer
you get 4x-2

Answer 5

u can not find them u have to know them : inverse of sin(x) is the arcsin x, log x the e^x