Determine algebraically if f(x) =(7x-2) / (4). And g(x) = (4x+2) / (7) are inverse functions. Show how you know,

Question

I do not understand this type of problem i have a test on these tmrw and need some help with how to figure these out pls help.

Answer 1

f and g are inverse functions if

f(g(x)) = g(f(x)) = x

f(g) = (7g-2)/4 = (4x+2-2)/4 = x
g(f) = (4f+2)/7 = (7x-2+2)/7 = x

Answer 2

Is this the answer or should i go further? Sorry im very lost

Answer 3

Alternate way:

find inverse of f(x) to see if you get g(x)
let y = f(x) = (7x-2)/4
the inverse is :
x = (7y-2)/4
4x = 7y - 2
4x + 2 = 7y
y = (4x+2)/7 which is the given g(x)

so yes, they are inverses of each other.