one to one functions

Question

The one-to-one functions g and h are defined as follows.

g= {(-6,6),(-5,3),(-3,7),(7,9)}

h(x)=2x+3

Find the following.

g^-1 (7) = ?

h^-1 (x) = ?

(h^-1 o h)(-5) = ?

Answer 1

If y = f(x) is a one-to-one function, then f^-1(x) exists.

For such a function, If f(a) = b, then f^-1(b) = a

So, since g(x) is one-to-one and g(-3) = 7, g^-1(7) = -3

To find h^-1(x) let y = 2x + 3. Switch x and y then solve for y to get y = (x - 3) / 2 = h^-1(x)

(h^-1 o h)(5) = h^-1(h(5)) = h^-1(13) = 5

Answer 2

The power -1 means 1/.

g^-1=1/g=1/7.