Determine by the composition whether f(x)=1/5 x+4 and g(x)=5x-20 are inverses

composition-inverses

#1

Determine by the composition whether f(x)=1/5 x+4 and g(x)=5x-20 are inverses.

Answer:

Assuming f(x) = (1/5)x + 4, then
f(g(x)) = (1/5)(5x - 20) + 4
= x - 4 + 4
= x

Hence, f and g are inverses.

If I recall correctly, if f(g(x)) = x then g(f(x)) = x also. Nonetheless, you might find it instructive to show that g(f(x)) = x for the given f and g.

f(x) is a function. f^(-1)x is inverse function of f(x)
y=f(x) ; f^(-1)(y)=x
f(x)=y=(1/5)x+4
y-4=1(/5)x
5(y-4)=x
x=inverser of f(x)= f^(-1)(y)=5y-20 ; f^(-1)x=5x-20 which is g(x)
so if we do find g^(-1)x inverse of g(x) , we get (1/5)x+4 which is f(x).
Hence f(x) and g(x) are inverses.