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LiRa [457]
2 years ago
11

Which pair of expressions represents inverse functions

Mathematics
2 answers:
Natali5045456 [20]2 years ago
7 0

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


s344n2d4d5 [400]2 years ago
5 0

Answer:

<h2>C.</h2>

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.

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