Question

Which pair of expressions represents inverse functions

Answer 1

Answer: C. $\dfrac{x+3}{4x-2}$ and $\dfrac{2x+3}{4x-1}$

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)=$\dfrac{x+3}{4x-2}$ and g(x)=$\dfrac{2x+3}{4x-1}$

   fog(x)=f($\dfrac{2x+3}{4x-1}$)

              =$\dfrac{\dfrac{2x+3}{4x-1}+3 }{\dfrac{4(2x+3)}{4x-1}-2 }$

               =x

   gof(x)=g($\dfrac{x+3}{4x-2}$)

              =$\dfrac{\dfrac{2(x+3)}{4x-2} +3}{\dfrac{4(x+3)}{4x-2}-1 }$

               =x

hence C. is the pair of inverse functions

Answer 2

Answer:

C.

Step-by-step 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.

$f(x)=\frac{x+3}{4x-2}\\ g(x)=\frac{2x+3}{4x-1}$

$f(g(x))=\frac{(\frac{2x+3}{4x-1})+3}{4(\frac{2x+3}{4x-1} )-2} \\f(g(x))=\frac{\frac{2x+3+12x-3}{4x-1}}{\frac{8x+12}{4x-1}-2 }\\ f(g(x))=\frac{\frac{2x+3+12x-3}{4x-1} }{\frac{8x+12-8x+2}{4x-1} } =\frac{14x}{14}=x$

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