SOLUTION: for the one to one function f(X)=x+1/2x-3 a)find the inverse f^-1 f(x)=x+1/2x-3 y=x+1/2x-3 x=y+1/2y-3 divide 2y-3 on both sides =(2y-3)x=y+1 -1 from both sides =2xy-1-3x=y-2

Algebra ->  Trigonometry-basics -> SOLUTION: for the one to one function f(X)=x+1/2x-3 a)find the inverse f^-1 f(x)=x+1/2x-3 y=x+1/2x-3 x=y+1/2y-3 divide 2y-3 on both sides =(2y-3)x=y+1 -1 from both sides =2xy-1-3x=y-2      Log On


   

Question 1139660: for the one to one function f(X)=x+1/2x-3
a)find the inverse f^-1
f(x)=x+1/2x-3
y=x+1/2x-3
x=y+1/2y-3
divide 2y-3 on both sides
=(2y-3)x=y+1
-1 from both sides =2xy-1-3x=y-2xy
factor out y-2xy=-1-3x=y(1-2x)
divide 1-2x on both sides =y=-3x-1/-2x+1
-1/-1(y=3x+1/2x-1
f^-1=3x+1/2x-1
Now graph f and graph f^-1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a)find the inverse f%5E-1
f%28x%29=x%2B%281%2F2%29x-3.....replace f%28x%29 with y
y=x%2B%281%2F2%29x-3.......swap x and y
x=y%2B%281%2F2%29y-3....solve for y
x%2B3=y%2B%281%2F2%29y
x%2B3=y%281%2B1%2F2%29
x%2B3=y%283%2F2%29
x%2F%283%2F2%29%2B3%2F%283%2F2%29=y
y=%282%2F3%29x%2B6%2F3
y=%282%2F3%29x%2B2
=>f%5E-1=%282%2F3%29x%2B2
graph:
yu need two points on a line; so, choose x and find f%5E-1
x|f%5E-1
0|2
3|4
plot points and draw a line through