the function f(x)=4/x-7 is one to one
a. find the inverse of f
b. graph f, f^-1, and y=x on the same set of axes
find the inverse of f
f^-1(x)=
y = 4/x - 7
x = 4/(y+7)
so, f(x) = 4/x - 7
f^-1(x) = 4/(x+7)
do the graphs here:
http://rechneronline.de/function-graphs/
If yu meant y = 4/(x-7), of course, things are different.
To find the inverse of a function, you can follow these steps:
Step 1: Replace the function notation f(x) with y.
y = 4/x - 7
Step 2: Swap the x and y variables.
x = 4/y - 7
Step 3: Solve the equation for y.
x + 7 = 4/y
Cross-multiply:
xy + 7y = 4
Step 4: Rearrange the equation to get y by itself.
xy = 4 - 7y
xy + 7y = 4
y(x + 7) = 4
y = 4 / (x + 7)
So, the inverse of f(x) = 4/x - 7 is f^(-1)(x) = 4 / (x + 7).
Now, let's move on to graphing.
To graph f, f^(-1), and y = x on the same set of axes, follow these steps:
Step 1: Choose a range of x-values to plot. Let's say -10 ≤ x ≤ 10.
Step 2: Calculate the corresponding y-values for each function using the given equations.
For f(x) = 4/x - 7:
Choose some x-values within the range, calculate the corresponding y-values using the equation f(x) = 4/x - 7.
For f^(-1)(x) = 4 / (x + 7):
Choose the same set of x-values, but this time calculate the corresponding y-values using the equation f^(-1)(x) = 4 / (x + 7).
For y = x:
For each x-value within the range, the y-value will be the same as the x-value.
Step 3: Plot the points for each equation on the graph.
Step 4: Connect the points for each equation to create the corresponding graphs.
Step 5: Label each graph accordingly (f, f^(-1), and y = x).
This will give you a graph that includes f(x), f^(-1)(x), and the line y = x on the same set of axes.