Question

If f∘g(x)=g∘f(x) , then f and g are inverse of each other. True or False

Answer 1

The given statement is

$f\circ g(x)=g\circ f(x)$

Are inverse of each other

Since the function and its inverse are symmetric around the line y = x, then

$f\circ g(x)=g\circ f(x)=x$

Then the statement above is false because f(x) and g(x) are inverse functions if

$f\circ g(x)=g\circ f(x)=x$

It is False

f(x) is the red graph

Its inverse is the blue graph

The green line is y = x

The red and the blue graph are symmetric around the line y = x

So if f(g (x) = g(f(x)) = x

Then f(x) and g(x) are inverse function