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consider f(x)= square root of x^2-1 and g(x) = square root of x^2+1. what values of x would make f(g(x)) and g(f(x)) cumulative

Sagot :

Cumulative probability is a random variable determined by adding the probability density functions altogether, and its calculation can be defined as follows:

Cumulative function calculation:

  • Random variable distributions are described using the cumulative distribution function.
  • It can be applied to a discrete, continuous, or mixed variable to describe the probability.

Given:

[tex]\to f(x)= \sqrt{x^2-1} \\\\\to g(x) = \sqrt{x^2+1}[/tex]

Find:

[tex]\to f(g(x))[/tex] and [tex]g(f(x))[/tex]

[tex]\to f(g(x))[/tex]

[tex]\to f(\sqrt{x^2+1})\\\\\to \sqrt{\sqrt{(x^2-1)+1}} \\\\\to \sqrt{\sqrt{x^2-1+1}} \\\\\to \sqrt{\sqrt{x^2}} \\\\\to \sqrt{x}} \\\\[/tex]

[tex]\to g(f(x))\\\\\to g(\sqrt{x^2-1})\\\\\to \sqrt{\sqrt{(x^2+1)-1}} \\\\\to \sqrt{\sqrt{x^2+1-1}} \\\\\to \sqrt{\sqrt{x^2}} \\\\\to \sqrt{x} \\\\[/tex]

Find out more about the cumulative function here:

brainly.com/question/15353924