Question

How to solve question 2(a,b,c)?​

Answer 1

a) For h(2)=5 then k=4

b) For h(3)=k then k=3

c) For h(k)=k then k=3

Explanation:

Given that the function h is defined by

`h(x)=(kx-3)/(x-1)` where
`x\\eq1`

a) To find for h(2)=5:

`h(x)=(kx-3)/(x-1)` where
`x\\eq1`

that is put x=2 in the above function

`h(2)=(k(2)-3)/(2-1)=5`

Now
`(2k-3)/(1)=5`

`2k-3=5`

`2k=5+3`

`k=(8)/(2)`

k=4

Therefore k=4

b) To find for h(3)=k:

`h(x)=(kx-3)/(x-1)` where
`x\\eq1`

that is put x=3 in the above function

`h(3)=(k(3)-3)/(3-1)=k`

Now
`(3k-3)/(2)=k`

`3k-3=2k`

`3k-2k-3=0`

`k-3=0`

k=3

Therefore k=3

c) h(k)=k

To find for h(3)=K:

`h(x)=(kx-3)/(x-1)` where
`x\\eq1`

that is put x=k in the above function

`h(k)=(k(k)-3)/(k-1)=k` here
`k\\eq1`

Now
`(k^2-3)/(k-1)=k`

`k^2-3=k(k-1)`

`k^2-3=k^2-k`

`k^2-3-k^2+k=0`

k-3=0

k=3

Therefore k=3