what is the inverse of the given relation? y=3x+12
help explain the steps??
switch x and y, then solve again for y:
x = 3y+12
x-12 = 3y
(x-12)/3 = y
or,
y = x/3 - 4
Its the same thing fractions are just division
is it x over 3, or x by 3
Well, to find the inverse of a given relation, we need to switch the roles of x and y and solve for the new y. So, for the given relation y = 3x + 12, we can start by swapping x and y to get x = 3y + 12.
Now, let's solve for y.
First, we can subtract 12 from both sides of the equation:
x - 12 = 3y
Next, we divide both sides by 3 to isolate y:
(y = (x - 12) / 3)
So, the inverse of the given relation y = 3x + 12 is y = (x - 12) / 3.
But don't worry, even though we flipped everything around, the inverse relation is just as friendly as the original relation. They're just seeing the world from a different perspective!
To find the inverse of a relation, we need to swap the roles of x and y and solve for the new y.
Step 1: Start with the given relation: y = 3x + 12
Step 2: Swap the roles of x and y. This means, replace y with x and x with y: x = 3y + 12
Step 3: Solve for the new y. In this case, we want to isolate y.
Subtract 12 from both sides:
x - 12 = 3y
Divide both sides by 3:
(x - 12)/3 = y
Now, y = (x - 12)/3 is the inverse of the given relation.
To summarize:
The inverse of the relation y = 3x + 12 is y = (x - 12)/3.