the one-to-one function g and h are defined aas follows

Question

g=(-8,4),(-2,1),(0,5),(8,-8)

h(x)=x-9/7

find the following

g^-1(-8)=

h^-1(x)=

(h^-1.h)(-5)=

Answer 1

g(x)=y

g(8)=-8

for the inverse, switch x and y

g^-1(y)=x

g^-1(-8)=8

g = (x,y)

g^-1 = (y,x)

g = (-8,4), (-2,1), (0,5), (8,-8)

g^-1= (4,-8),(1,-2), (5,0), (-8,8)

h(x)=(x-9)/7

h(16)=(16-9)/7=7/7=1

subtract 9, then divide by 7

reverse the operations

multiply by 7, then add 9

h^-1(x)=7x+9

h^-1(1)=7(1))+9=7+9=16

or, if h(x)=x-(9/7)

subtract 9/7

h(9/7)=9/7-9/7=0

h^-1(0)=0+(9/7)=9/7

h^-1(x)=x+(9/7)

add 9/7

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

composite of inverse functions brings you back to where you started

h^-1(h(x))=x

h^-1(-5)=7(-5)+9=-35+9=-26

h(-26)=(-26-9)/7=-35/7=-5

h(-5)= (-5-9)/7= -14/7=-2

h^-1(-2)=7(-2)+9=-14+9=-5

functions are funky, not to be shunned

easy as 1 2 1