Respuesta :
The functions f(x) and g(x) are inverses of each other.
To Verify the Inverse of a Function
to Verify the Inverse of two functions we need to simply substitute the value of the first expression into another expression, whose result will at the end give us an x. for example, let's assume two functions f(x) and g(x), then
[tex]f(x) = \dfrac{1}{g(x)}[/tex]
if,
[tex]f[g(x)] = x[/tex]
Given to us,
f(x) = 5-3x/2,
g(x) = 5-2x/3,
Proof,
[tex]\begin{aligned}f[g(x)],\\f[g(x)]&= \dfrac{5-3( \dfrac{5-2x}{3})}{2}\\\\&= \dfrac{5-\dfrac{3}{3}( {5-2x})}{2}\\\\&=\dfrac{5-(5-2x)}{2}\\\\&= \dfrac{5-5+2x}{2}\\\\&=\dfrac{0+2x}{2}\\&=\dfrac{2x}{2}\\&=x\end{aligned}[/tex]
Hence, the functions f(x) and g(x) are inverses of each other.
Learn more about the inverse of function:
https://brainly.com/question/5245372
