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Question 3.13F
If the two functions are inverses, which of the following statements correctly verifies this?
f(x)=9x+9/7 and g(x)=7x+9/9

Question 313F If the two functions are inverses which of the following statements correctly verifies this fx9x97 and gx7x99 class=

Respuesta :

sqdancefan

Answer:

  (6)  The functions f and g are not inverses

Step-by-step explanation:

You want to know which of several statements proves f(x) = (9x+9)/7 and g(x)=(7x+9)/9 are inverses of each other.

Inverse functions

The inverse of f(x) can be found by solving ...

  x = f(y)

  x = (9y +9)/7

  7x = 9y +9

  7x -9 = 9y

  y = (7x -9)/9

The plus sign in f(x) turns into a minus sign in its inverse function. g(x) is not the inverse of f(x).

The functions f and g are not inverses.

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Additional comment

As answer choice (2) suggests, graphs of inverse functions will be reflections of each other in the line y=x. The attached graph shows they are not, hence f(x) is not the inverse of g(x).

Ver imagen sqdancefan

The correct statement that correctly verifies the two functions f(x) = (9x + 9) / 7 and g(x) = (7x + 9) / 9 is the functions f and g are not inverses

How to get inverse of a function

The inverse of a function is solved by making the input function equal to the output function

the inverse of f(x) = (9x + 9) / 7

f(x) = y = (9x + 9) / 7

7y = 9x + 9

9x = 7y - 9

x = (7y - 9) / 9

changing the input and output of the new functions

hence f⁻¹ =  (7x - 9) / 9

Since f⁻¹ ≠ g(x) the last option is the correct option

Learn more about inverse functions at:

https://brainly.com/question/11735394

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