Answer:
(a) f and g are inverse of each other
(b)f and g are inverse of each other.
Step-by-step explanation:
These are the conditions for two functions f and g to be inverses:
(a) Given
[tex]f(x) = \frac{1}{3x}, x\neq0\\g(x) = \frac{1}{3x}, x\neq0[/tex]
[tex]f(g(x)) = \frac{1}{3(\frac{1}{3x})} =\frac{1}{\frac{1}{x} }=x[/tex]
[tex]g(f(x)) = \frac{1}{3(\frac{1}{3x})} =\frac{1}{\frac{1}{x} }=x[/tex]
Since f(g(x))=g(f(x))=x, f and g are inverses of each other.
(b)Given:
f(x)=x+4
g(x)=x=4, i.e.g(x)=x-4
f(g(x))= (x-4)+4 =x
g(f(x))=(x+4)-4 =x
Since f(g(x))=g(f(x))=x, f and g are inverses of each other.
