To find: The inverse of the given function.
Step 1: Substitute y=f(x). We get
y2=4x+3. By solving this equation for x, we get the expression x=y2-34.
Step 2: Interchange the positions of x and y, we get y=x2-34
Graphs for f, f-1andy=x:
The orange-colored graph represents the function f-1. The blue-colored graph represents the function f. The green-colored graph represents the line y=x.
First draw the line y=x and the graph of f. Then take the mirror image of f about the line y=x. You can observe that the graphs for functions f-1 and f are symmetrical about the line y=x.
Final Staetement: f-1x=x2-34