SOLUTION: Given F(x) shown below, complete the equation for the inverse of F(x). If necessary, use the slash mark ( / ) for the division symbol. f(x)=2x/7+4 F-1(y) = _____ Answe

Algebra ->  Inverses -> SOLUTION: Given F(x) shown below, complete the equation for the inverse of F(x). If necessary, use the slash mark ( / ) for the division symbol. f(x)=2x/7+4 F-1(y) = _____ Answe      Log On


   

Question 205044: Given F(x) shown below, complete the equation for the inverse of F(x). If necessary, use the slash mark ( / ) for the division symbol.
f(x)=2x/7+4


F-1(y) = _____
Answer:

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
f%28x%29+=+2x%2F7+%2B4 find the inverse. First, replace f%28x%29 with y
y+=+2x%2F7+%2B4 Now exchange the variables x and y.
x+=+2y%2F7%2B4 then solve this equation for y. Subtract 4 from both sides.
x-4+=+2y%2F7 Multiply both sides by 7.
7x-28+=+2y and divide both sides by 2.
y+=+%287x-28%29%2F2 Finally, replace y with f%5E-1%28x%29
highlight%28f%5E-1%28x%29+=+%287x-28%29%2F2%29
By the way, notice that it is f%5E-1%28x%29 and not f%5E-1%28y%29