Begin by replacing f(x) with y. Then, exchange x and y in the equation and solve it for y.
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Practice makes perfect
Analyze the given function, determine its inverse and graph. Then, compare it to the given graphs. To algebraically determine the inverse of f(x), we need to first replace f(x) with y. After that, exchange x and y and then, solve for y.
y= x+4 → x= y+4
The resultant equation will be the inverse of the given function, so let's solve for y.
To write the inverse function of f(x), replace y by f^(- 1)(x).
f^(- 1)(x)=x-4
To graph the equation, we will plot two points and connect them with a straight line. The first point is where the line will intercept the y-axis, at (0,- 4). To plot another point, we can use the slope, 1. By moving 1 step horizontally in the positive direction and 1 step vertically in the positive direction, we get another point.
In the graph, we can see that the inverse function passes through the points (4,0) and (0,-4). When comparing it with the given graphs, we see that it does not match any option. Therefore, none of the options given are correct.
Alternative Solution
If the function was f(x)=x+8
In this case, we will analyze the function f(x)=x+8, determine its inverse and graph. Then, compare it to the given graphs. To algebraically determine the inverse of f(x), we need to first replace f(x) with y. After that, exchange x and y and then, solve for y.
y= x+8 → x= y+8
The resultant equation will be the inverse of the given function, so let's solve for y.
To write the inverse function of f(x), replace y by f^(- 1)(x).
f^(- 1)(x)=x-8
To graph the equation, we will plot two points and connect them with a straight line. The first point is where the line will intercept the y-axis, at (0,-8). To plot another point, we can use the slope, 1. By moving 1 step horizontally in the positive direction and 1 step vertically in the positive direction, we get another point.
