Determine algebraically whether or not f(x)=7x-2/4 and g(x)=4x+2/7 are inverse functions
We can determine if f(x) and g(x) are inverse functions by checking if f(g(x)) = x and g(f(x)) = x.
First, let's find f(g(x)):
f(g(x)) = f(4x + 2/7)
= 7(4x + 2/7) - 2/4
= 7(4x) + 7(2/7) - 2/4
= 28x + 2 - 1/2
= 28x + 3/2
Now, let's find g(f(x)):
g(f(x)) = g(7x - 2/4)
= 4(7x - 2/4) + 2/7
= 28x - 1 + 2/7
= 28x - 5/7
Since f(g(x)) = 28x + 3/2 and g(f(x)) = 28x - 5/7, we can see that f(g(x)) is not equal to x and g(f(x)) is not equal to x.
Therefore, f(x) = 7x - 2/4 and g(x) = 4x + 2/7 are not inverse functions.