Respuesta :
They switched the 1/x to a positive and the added 5x. The domains are 1, 2, 3, 4, -5, -4, -3, -2, -1, 0. Hope this helps.
Answer with explanation:
If f(x) and g(x) are two functions which are Inverses of each other then
either of two will be true.
→fog(x)=x
→ gof (x)=x
⇒fog(x)
=f[g(x)]
[tex]=f(\frac{5 x+1}{x})\\\\=f({5+\frac{1}{x}})\\\\=\frac{1}{({5+\frac{1}{x}-5})}\\\\=\frac{1}{\frac{1}{x}}\\\\=x[/tex]
→ gof (x)
=g[f(x)]
[tex]=g(\frac{1}{x-5})\\\\=5+\frac{1}{\frac{1}{x-5}}\\\\=5+x-5\\\\=x[/tex]
Which shows that f(x) and g(x) are inverses of each other.
→Domain of f(x)= All Real numbers excluding 5=R-{5}
→Domain of g(x)=All Real numbers excluding 0=R-{0}
→Domain of fog(x)=All Real numbers
