Question

one to one functions g and h are defined as follows.
g={ (-8,6), (-4,5), (5,8), (9,3)}
h (x)= 2x-3

and I have to find the following of:
1.) g^-1 (5) = ?
2.) h^-1 (x) =?
(h o h^-1) (2)= ?

(I don't understand the steps to finding these answers..)

Answer 1

g^-1 (5) is asking

what value of x will produce y = 5 when you plug it into g(x)?

Answer 2

well that's x = -4 since we have the ordered pair (-4, 5)

ie when x = -4, y = 5 in g(x)

so,

g^-1 (5) = -4

Answer 3

ok i understand that one

Answer 4

h^-1(x) is the inverse of h(x)

so you need to find the inverse for part 2

Answer 5

do you know how to do that?

Answer 6

i see what your saying i don't know how to find the inverse of 2x-3 though..

Answer 7

h(x) = 2x - 3

y = 2x - 3 ... replace h(x) with y

x = 2y - 3 ... swap x and y

now solve for y

Answer 8

so would you add the 3 to x and divide both by 2?

Answer 9

i got y=x/2+3/2

Answer 10

good

Answer 11

so that's the inverse function

h^-1(x) = x/2 + 3/2

you can optionally write it as

h^-1(x) = (x + 3)/2

Answer 12

im not sure what the last one is asking me to do

Answer 13

(h o h^-1) (2) is the same as saying h( h^-1(2) )

Answer 14

so am i plugging 2 into x

Answer 15

you are plugging 2 into the inverse and getting some result...call this result z

you then take this result and plug it into the function h(x)

ie you are finding h(z)

Answer 16

so im plugging 2.5 into h(x)?

Answer 17

yep

Answer 18

so would 2 be the answer

Answer 19

correct, it turns out that because h(x) is linear, this means

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

is true for all values of x

Answer 20

ok thank you im starting to understand what these are asking!

Answer 21

you're welcome