Mathematics: A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.

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A. Use composition to prove whether or not the - id7303883, brendacauani12345

oportela23

31.01.2022

Step-by-step explanation:

A). If a function 'f' is inverse of another function 'g',

Then f[g(x)] = x = g[f(x)]

In this question the given functions are,

f(x) = $\frac{1}{x-3}$ and g(x) = $\frac{3x+1}{x}$

Then, f[g(x)] = $\frac{1}{\frac{3x+1}{x}-3}$

= $\frac{x}{3x+1-3x}$

= x

Similarly, g[f(x)] = $\frac{(\frac{3}{x-3})+1}{\frac{1}{x-3} }$

= $\frac{3+x-3}{1}$

= x

Therefore, Both the functions are inverse of each other.

B). Domain of the compositions of these functions will be a set of all real numbers, (-∞, ∞)

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