OpenStudy (anonymous):

Find an equation for the inverse of the function. f(x)=2-3x/4

3 years ago
OpenStudy (gorv):

find value of x

3 years ago
OpenStudy (gorv):

move everything on left side excpt x

3 years ago
OpenStudy (gorv):

f(x)-2=-3x/4 (f(x)-2)*(-4)/3=x now replace x by f^-1(x) and f(x) by x

3 years ago
OpenStudy (ybarrap):

1st step - write in terms of y y=2-3x/4 2nd step (interchange x and y): x=2-3y/4 3rd stop - solve for y x -2=-3y/4 -3y/4 = x - 2 -3y = 4(x-2) y=-4(x-2)/3 This is your inverse. Check you work by plugging in for x your original equation, f(x), you should get x back as result. That is what inverse means, you give it f(x) and you get x back. You give it a x and you get f(x) back: $$y=-4(2-\cfrac{3x}{4}-2)/3\\ =\cfrac{3x}{3}=x$$ You can also plug in for x the inverse we just derived into your original equation and you will get back f(x). I'll let you check that one.

3 years ago