Question #8e6ef

1 Answer

Answer:

To find the inverse of any function, you can follow these general steps:

1) Change the function notation f(x), g(x) etc. to y =
2) Interchange x and y : that is, swap the x's and the y's
3) Isolate for y
4) Put inverse back into function notation using # f^(-1)(x) # to represent the inverse

Explanation:

In your example you have #h(x) = 4/(-x-3) + 1#:

1) Change the function notation f(x), g(x) etc. to y = :

Simple: Let h(x) = y and thus,

# y = 4/(-x-3) + 1#

2) Interchange x and y : that is, swap the x's and the y's:

# x = 4/(-y-3)+1#

3) Isolate for y :

Subtract 1 from both sides:

# x-1 = 4/(-y-3) #

Multiply by (-y-3) on both sides to get y on top and on the left:

# (x-1)(-y-3) = 4 #

Divide by (x-1) on both sides:

# -y-3 = 4/(x-1)#

Add 3 to both sides:

-y = 4/(x-1)+3

Now, divide by -1 on both sides to get:

#y = -4/(x-1)+3#

4) Put inverse back into function notation using # f^(-1)(x) # to represent the inverse :

# h'(x) = -4/(x-1)+3 #

And that's your inverse! Hopefully things were clear! Should you have any questions, feel free to ask! :)