FIND f(g(x)) and g(f(x)) and determine wether the pair of functions f and g are inverses of each other?

f(x) = 7x - 4

g(x) = x + (7/4)

f(g(x)) just means plug [x + (7/4)] where their is

an x in the f function therefore

f(g(x)) = 7[x + (7/4)] - 4

7x + (49/4) - (4)

7x + (49/4) - (16/4)

7x + (33/4)

g(f(x)) just means plug (7x - 4) where their is

an x in the g function therefore

g(f(x)) = (7x - 4) + (7/4)

7x - (16/4) + (7/4)

7x - (9/4)

To find if there inverse make

one of the equations set to the answer y

y = 7x + (33/4)

now switch the variable

x = 7y + (33/4)

solve for y

x = 7y + (33/4)

x - (33/4) = 7y

y = (x/7) - (33/28)

There not inverse functions of each other

f(g(x)) 〓 7(x+7/4) - 4 〓 [(7x + 49)/4] - 4

g(f(x)) 〓 (7x-4+7)/4 〓 (7x+3)/4

The inverse of y 〓 7x - 4 is defined as x 〓 7y - 4 and isolating y produces y 〓 (x+4)/7 which is not g(x).

If the fuctions were inverses then f(g(x)) 〓 g(f(x)) 〓 1.