Given [tex]f(x) = 3x - 2[/tex] and [tex]g(x) = -\frac{1}{3}x + \frac{2}{3}[/tex], determine if [tex]g(x)[/tex] and [tex]f(x)[/tex] are inverse functions.
Answer (2)
When dealing with inverse functions, I like to put them in terms of x and y to make it easier. y=3x-2 and y=-1/3x+2/3 to find the inverse of a function, one method is to switch the variables and then solve for the same variable as the first time, so the inverse of y=3x-2 is x=3y-2, which we now solve for y again. x=3y-2 => x+2=3y => y=1/3x+2/3 which is not the same as y=-1/3x+2/3 Final answer: No, f(x) and g(x) are not inverse functions. Hope I could help :)
The functions f ( x ) = 3 x − 2 and g ( x ) = − 3 1 x + 3 2 are not inverse functions because their compositions do not yield the identity function (i.e., they do not return x ). Specifically, f ( g ( x )) = − x and g ( f ( x )) = − x + 3 4 . Therefore, they do not satisfy the conditions for being inverses of each other.
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