How to find one-to-one functions g and h

g={(-3,-5), (-1,1), (3,-1), (4,3)}

h(x)=4x+13

Find the Following..

g^-1(3)=
h^1(x)=
(h o h^-1) (-3)=


Please help! I remember learning it but I can't remember how to do it, it's been so long! Thanks!

(a) g^-1(3):
By the definition of the inverse function:
g(x) = y implies g^-1(y) = x.

This basically says that to find the inverse function of g(x), we just swap the x and y-coordinates. Upon doing this, we see that:
g^-1(x) = {(-5, -3), (1, -1), (-1, 3), (3, 4)}.

Thus, g^-1(3) = 4.

(b) h^-1(x):
To find the inverse function of h(x), interchange x and y and re-solve for y. Letting h(x) = y gives:
y = 4x + 13.

Interchanging x and y:
x = 4y + 13.

Re-solving for y:
y = h^-1(x) = (x - 13)/4.

(c) (h o h^-1)(-3):
By the definition of the inverse function, if f(x) and g(x) are inverses, then:
(f o g)(x) = (g o f)(x) = x.

Therefore:
(h o h^-1)(-3) = -3.

I hope this helps!