First find the equation of f(x). To do this you need to know its slope and a point on the line.
f^(- 1)(x)=1/4x+3/4
Practice makes perfect
First we will find the equation for f(x). Then, we will use that to find the inverse function.
Finding the Equation of f(x)
We know that the slope of f(x) is 4. Let's write this into its equation.
f(x) = mx+b ⇒ f(x) = 4x+b
Now we need to find a point that f(x) passes through. Since we know that the inverse function f^(-1)(x) passes through the point ( 5, 2), we can find such a point by interchanging the x- and y-coordinates.
Point on f^(- 1)(x)
Point on f(x)
( 5, 2)
( 2, 5)
Now we can determine f(x) by substituting the point into the equation of f(x) and solve for b.
We already know one point on the inverse function. But we need to find another one to be able to write its equation. To find such a point we will use f(x). We will now draw its graph. We will also mark the point ( 2, 5) and and its y-intercept (0,- 3).
By interchanging the x- and y-coordinates of the y-intercept we find a second point that f^(- 1)(x) passes through.
Point on f(x)
Point on f^(- 1)(x)
( 0, - 3)
( - 3, 0)
We now know two points on the graph of the inverse function. By using the Slope Formula we can calculate its slope.
The slope of the inverse function is 14. Let's write this into its equation.
f^(-1)(x)=mx+b ⇒ f^(-1)(x)= 1/4x+b
Now we can determine the inverse function by substituting one of the known points into the equation and solving for b.
