If #f ( x ) = 3x - 4 and g ( x ) = \frac { x + 4} { 3}#, how do you verify if #f(x) and g(x) are inverse functions?

1 Answer
Dec 14, 2017

If f(x) and g(x) are inverse functions, then f(g(x)) = x and g(f(x)) = x.

so, to verify if 2 functions are inverse, substitute the value for one function as the variable in the definition of the other function. As a practical mater, you can go either way, f(g(x)) or g(f(x)), whichever is computationally easiest. If you get back 'x', then you're done.

So, for example, we'll substitute the value of f(x), 3x -4, as the variable in the definition of g(x). In other words, in the formula for g(x), substitute #3x-4# wherever you see #x#:

#((3x-4)+4)/3 = #

#(3x)/3 = #


...and you can color it done. GOOD LUCK