What is the inverse of the function f(x) = 2x + 1?

2 Answers
Feb 20, 2018

#y=0.5(x-1)#

Explanation:

To find the inverse of a function, you have to substitute #y# for #x# in the equation and simplify to get a normal equation again. In this case, #f(x)# is #y#.

#y=2x+1#

#x=2y+1#

#2y+1=x#

#2y=x-1#

#y=0.5(x-1)#

So there you have it.

Feb 20, 2018

#f^(-1)(x)=(x-1)/2#

Explanation:

#f(x)=y#

#y=2x+1#

Switch the places of x and y:

#x=2y+1#

Now, solve for y so the function is once again written in terms of x:

#2y=x-1#

#y=(x-1)/2#

#f^(-1)(x)=(x-1)/2#

Where #f^(-1)(x)# denotes that the function is an inverse of the original function.