Question

g=[(-7,-5) , (-4,-7) , (5,0) , (9,6)]
h(x)=2x-3

find g^-1(-7)=?
h^-1(x)=?
(h times h^-1)(3)=?

Answer 1

\[g(-4)=-7\] so \[g^{-1}(-7)=-4\]

Answer 2

h says mulitiply by 2, subtract 3 so
\[h^{-1}\] will say add 3 divide by 2
\[h^{-1}(x)=\frac{x+3}{2}\]

Answer 3

if that is too annoying think about solving this
2x+3=11 steps are subtract 3 divide by 2 to get x = 4
now if we have y = 2x +3 and we want to solve for x we write
y - 3 = 2x or x = (y-3)/2 and that is your inverse

Answer 4

and finally it is not times, it is "of"
not
\[h\times h^{-1}(x)\] but rather
\[h(h^{-1}(x))\]
and
\[h(h^{-1}(x))=x\] because when you compose a function with its inverse you get what you started with