Respuesta :

s384811

Answer:

A

Step-by-step explanation:

Inverse means that the function is reversed from the original function, f(x).

To find the inverse function of f(x)=5x-11, add 11 to x, then divide the expression by 5.

This would be (x+11)/5.

So, you know that A is true.

Try the other selections too.

B: [tex]g(x)=x^3/2[/tex]       The x should be tripled before being divided by 2; FALSE

C: [tex]g(x)=7/(x+9)[/tex]     7 should by in the numerator; FALSE

D: [tex]g(x)=6(x+8)[/tex]    8 should be added before being multiplied by 6; FALSE

I hope this helps!!!

Using composite functions, it is found that the pair of functions that are inverse of each other is given by:

A. [tex]f(x) = 5x - 11[/tex] and [tex]g(x) = \frac{x + 11}{5}[/tex]

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The composite of functions f and g is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

Two functions f and g are inverse of each other if:

[tex]f(g(x)) = g(f(x)) = x[/tex]

Item a:

[tex]f(x) = 5x - 11[/tex]

[tex]g(x) = \frac{x + 11}{5}[/tex]

[tex]f(g(x)) = f(\frac{x + 11}{5}) = 5(\frac{x + 11}{5}) - 11 = x + 11 - 11 = x[/tex]

[tex]g(f(x)) = g(5x - 11) = \frac{5x - 11 + 11}{5} = \frac{5x}{5} = x[/tex]

Since [tex]f(g(x)) = g(f(x)) = x[/tex], these functions are inverse of each other.

A similar problem is given at https://brainly.com/question/23458455

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