Verifying Inverse Functions In Exercises 1316 verify that f

Verifying Inverse Functions In Exercises 13-16, verify that f and g are inverse functions. f(x) = -7/2x - 3, g(x) = - 2x + 6/7

Solution

given f(x)=-(7/2)x -3 ,g(x)=-(2x+6)/7

(fog)(x)

=f(g(x))

=f(-(2x+6)/7)

=-(7/2)(-(2x+6)/7) -3

=((2x+6)/2) -3

=x+3 -3

=x

(gof)(x)

=g(f(x))

=g(-(7/2)x -3)

=-(2(-(7/2)x -3) +6)/7

=-((-7x -6) +6)/7

=-(-7x)/7

=7x/7

=x

(fog)(x)=(fog)(x) =x

so f and g are inverse functions