How do you graph #f(x)=2x+1# and then use the horizontal test to determine whether the inverse of f is a function?

1 Answer
VNVDVI
Feb 20, 2018

Find your intercepts, connect and continue in each direction, draw a horizontal line through various points of the graph and make sure it never intersects more than once.

Explanation:

Find the x and y intercepts of #f(x)#:

y-intercept:

#f(0)=2(0)+1=1#

#(0,1)# is our y-intercept.

#2x+1=0#

#2x=-1# #x=-1/2#

#(-1/2,0)# is our x-intercept.

Plot these two points on the graph, connect them, and continue in each direction.

graph{2x+1 [-7.9, 7.9, -3.95, 3.95]}

For the inverse of f(x) to be a function, a horizontal line drawn through the graph of #f(x)# at any given point should intersect the graph no more than once.

Here, we can see that would certainly apply.

enter image source here

Thus, the inverse of #f(x)#, denoted by #f^(-1)(x)#, is a function.

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