We can determine if two functions, f and g, are inverse functions by checking if the composition of f and g and the composition of g and f is the identity function, f(g(x)) = x and g(f(x)) = x.
First, we check the composition f(g(x)):
f(g(x)) = f(x + 2/3)
= 3(x + 2/3) - 2
= 3x + 2 - 2
= 3x
Since f(g(x)) = 3x, which is not equal to x, f and g are not inverse functions.
Second, we check the composition g(f(x)):
g(f(x)) = g(3x - 2)
= 3x - 2 + 2/3
= 3x - 2/3
Since g(f(x)) = 3x - 2/3, which is not equal to x, g and f are not inverse functions.
Therefore, f(x) = 3x - 2 and g(x) = x + 2/3 are not inverse functions.
Determine algebraically whether f(x)=3x-2 and g(x)= x+2/3 are
inverse functions.
3 answers
Rewrite the following set: {x|-11 ≤ x < 8} in interval notation.
The set {x|-11 ≤ x < 8} can be rewritten in interval notation as [-11, 8).