Find the inverse of the relation; {(-1,3),(2,5),(-3,5),(2,0)}...?

Question

{(-1,3),(2,5),(-3,5),(2,0)} is the relation, find the inverse.

Then write an equation of the inverse relation of y=3x+5.

Let me know what you get on each of the above. I'm trying to check work and want to see if my line of working is correct. Thank you!

*** one more: write an equation of the inverse relation to y=5x^2-4.

Answer 1

Reverse the ordered pairs. (-1,3) becomes (3, -1).

Replace x with y and y with x. Solve for y.

x = 3y + 5 3y = x - 5 y = (x - 5) / 3

x = 5y^2 - 4 5y^2 = -x - 4 y^2 = - x - 4 / 5

y = Sq rt -x - 4 / 5

Answer 2

Y=(x/3)-(5/3)

Answer 3

inverse : {(3,-1),(5,2),(5,-3),(2,0)}
y = f(x) = 3x+5 -> y-5=3x -> y/3 - 5/3 = x ->f^-1(x) = x/3 - 5/3
to find the inverse of function that you can calculate y from x change that function to find x from y.