You can put this solution on YOUR website! g(x) = 2x - 5 is the equation of a line and is a function because there is only one value of y for each value of x.
The inverse function of g(x) is found by:
Solving for x.
Replacing x with y and y with x.
Let y = g(x)
Your equation becomes y = 2x - 5
Solve for y.
subtract y from both sides of the equation to get:
0 = 2x - 5 - y
subtract 2x from both sides of the equation to get:
-2x = -y - 5
divide both sides of the equation by -2 to get:
x = y/2 + 5/2
Replace x with y and y with x to get:
y = x/2 + 5/2
If this is the inverse function, then both equations will be a reflection about the line y = x.
A graph of these equations and the equation of y = x is shown below:
If these are inverse functions, then:
f(g(x) = g(f(x)
Take f(g(x))
f(x) = 2x-5
g(x) = x/2 + 5/2
f(g(x) = f(x/2+5/2) = 2 * (x/2 + 5/2) - 5 = x + 5 - 5 = x
g(f(x) = g(2x-5) = (2x-5)/2 + 5/2 = x - 5/2 + 5/2 = x
We have f(g(x) = g(f(x) which confirms that these equations are inverse functions of each other.
Definition of a function states that you have a 1 to 1 mapping form x to y.
This happens with both these equations as shown in the graph.
