45.2k views
1 vote
Find the inverse of each function1. f(x) = 4/(x+2) - 22. f(x)= -2x^5 - 3

User Hayal
by
7.1k points

1 Answer

3 votes

We are given the following function:


f\mleft(x\mright)=(4)/(x+2)-2

we are asked to determine the inverse of this function. To do that we will first change the "f(x)" for "y":


y=(4)/(x+2)-2

Now we will switch "x" and "y", like this:


x=(4)/(y+2)-2

Now we solve for "y", first by adding 2 to both sides:


x+2=(4)/(y+2)

Now we multiply both sides by "y+2":


(y+2)(x+2)=4

Now we divide both sides by "x+2":


y+2=(4)/(x+2)

Now we subtract 2 to both sides:


y=(4)/(x+2)-2

Now we change "y" for the inverse of f(x), that is:


f^(-1)(x)=(4)/(x+2)-2

And thus we found the inverse. A similar procedure can be used for function 2.

User Sjagr
by
7.3k points