Answer: C. [tex]\dfrac{x+3}{4x-2}[/tex] and [tex]\dfrac{2x+3}{4x-1}[/tex]
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)=[tex]\dfrac{x+3}{4x-2}[/tex] and g(x)=[tex]\dfrac{2x+3}{4x-1}[/tex]
fog(x)=f([tex]\dfrac{2x+3}{4x-1}[/tex])
=[tex]\dfrac{\dfrac{2x+3}{4x-1}+3 }{\dfrac{4(2x+3)}{4x-1}-2 }[/tex]
=x
gof(x)=g([tex]\dfrac{x+3}{4x-2}[/tex])
=[tex]\dfrac{\dfrac{2(x+3)}{4x-2} +3}{\dfrac{4(x+3)}{4x-2}-1 }[/tex]
=x
hence C. is the pair of inverse functions
Answer:
Step-by-step explanation:
When two functions are inverse of each other, their composition must fulfil the following rule.
[tex]f(g(x))=x[/tex]
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.
[tex]f(x)=\frac{x+3}{4x-2}\\ g(x)=\frac{2x+3}{4x-1}[/tex]
[tex]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[/tex]
Therefore, the pair of functions which are inverse are the given by choice C.
