Question

Which pair of expressions represents inverse functions

Answer 1

C.

Explanation:

When two functions are inverse of each other, their composition must fulfil the following rule.

`f(g(x))=x`

That is, if we find their composition, the result must be the independent variable.

If you observe closely, the function given by choice C has some similarity, let's evaluate them to see if they are inverse functions.

`f(x)=(x+3)/(4x-2)\\ g(x)=(2x+3)/(4x-1)`

`f(g(x))=(((2x+3)/(4x-1))+3)/(4((2x+3)/(4x-1) )-2) \\f(g(x))=((2x+3+12x-3)/(4x-1))/((8x+12)/(4x-1)-2 )\\ f(g(x))=((2x+3+12x-3)/(4x-1) )/((8x+12-8x+2)/(4x-1) ) =(14x)/(14)=x`

Therefore, the pair of functions which are inverse are the given by choice C.

Answer 2

Answer: C.
`(x+3)/(4x-2)` and
`(2x+3)/(4x-1)`

Step-by-step explanation: if a function f(x) has g(x) as its inverse then it satisfies fog(x)=x and gof(x)=x

C. f(x)=
`(x+3)/(4x-2)` and g(x)=
`(2x+3)/(4x-1)`

fog(x)=f(
`(2x+3)/(4x-1)`)

=
`((2x+3)/(4x-1)+3 )/((4(2x+3))/(4x-1)-2 )`

=x

gof(x)=g(
`(x+3)/(4x-2)`)

=
`((2(x+3))/(4x-2) +3)/((4(x+3))/(4x-2)-1 )`

=x

hence C. is the pair of inverse functions