How do you verify that f(x)=3x+5; g(x)=1/3x-5/3 are inverses?
1 Answer
Feb 22, 2017
If
Explanation:
There are three ways to verify that these functions are inverse functions:
-
(f @ g)(x) = f(g(x)) = 3(1/3x-5/3)+5 = x-5+5 = x (g @ f)(x) = g(f(x)) = 1/3(3x+5)-5/3 = x + 5/3 - 5/3 = x Thereforef(x) and g(x) are inverse functions. -
Let
f(x) = y . Interchangex withy , then solve fory . You should getg(x) :x = 3y+5 ,x-5=3y ,y=1/3x - 5/3 = g(x) -
Graph both functions and the
y=x line. The functions should be reflections of each other across they=x line. This means for each point(a,b) fromf(x) there should be a(b,a) point ong(x) .