Question

Determine whether these two functions are inverses. Show your work please. f(x)= 1/x+4-9; g(x)=1/3x+9

Answer 1

Answer:  No they are not inverses.

Step-by-step explanation:

If they are inverses,  then the inverse of f(x) will equal g(x).

$y=\dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's:}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Solve for y:}\\x+9=\dfrac{1}{y+4}\\\\y+4=\dfrac{1}{x+9}\\\\y=\dfrac{1}{x+9}-4$

f⁻¹(x) ≠ g(x) so they are not inverses