Question

Determining weather two dung ions are inverse of each other

Answer 1

a)

Functions given:

`f(x)=(3)/(x)`
`g(x)=(3)/(x)`

Procedure

• f(g(x))

Substituing g(x) in the x present in f(x)

`f(g(x))=(3)/(((3)/(x)))`

Simplifying:

`f(g(x))=(3\cdot x)/(3)`
`f(g(x))=x`

• g(f(x))

Substituing f(x) in the x present in g(x)

`g(f(x))=(3)/(((3)/(x)))`

Simplifying

`g(f(x))=(3\cdot x)/(3)`
`g(f(x))=x`

Since f(g(x)) = g(f(x)) = x, the given equation and the computed inverse are really inverse functions.

b)

`f(x)=2x-7`
`g(x)=2x+7`

• f(g(x))

Substituing g(x) in the x present in f(x)

`f(g(x))=2\cdot(2x+7)-7`
`f(g(x))=4x+14-7`
`f(g(x))=4x+7`

• g(f(x))

Substituing f(x) in the x present in g(x)

`g(f(x))=2\cdot(2x-7)+7`
`g(f(x))=4x-14+7`
`g(f(x))=4x-7`

Then, these functions are NOT inverse.

Answer:

• a) ,f and g are inverses of each other

,

• b) f and g are not inverses of each other