Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (1 point)

f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.

Answer 1

1) Functions given:

x - 7
f(x) = ----------
x + 3

- 3x - 7
g(x) = ------------
x - 1


2)


`f[g(x)]=f[ (-3x-7)/(x-1)]= ( (-3x-7)/(x-1)-7 )/( (-3x-7)/(x-1)+3 ) = ( (-3x-7-7x+7)/(x-1) )/( (-3x-7+3x-3)/(x-1) ) = (-10x)/(-10) =x`

3)


`g[f(x)]=g[ (x-7)/(x+3)]= (-3[ (x-7)/(x+3)]-7)/( (x-7)/(x+3)-1 ) = ( (-3x+21-7x-21)/(x+3) )/( (x-7-x-3)/(x+3) )= (-10x)/(-10) =x`

So we have proved that f[g(x)]=g[f(x)]=x