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In order to prove that f(x) is inverse of g(x), we have to show f(g(x)) = g(f(x))

Question 1:

f(x) = -x/4 and g(x) = -4x

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

g(f(x)) = g(-x/4) = -4*(-x/4) = x

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

Hence f and g are inverses of each other.

Question 2:

f(x) = (x+3)/2 and g(x) = 2x+3

f(g(x)) = f(2x+3) = (2x+3+3)/2 = x+3

g(f(x)) = g((x+3)/2) = 2*(x+3)/2 +3 = x+6

As f(g(x)) is not equal to g(f(x))

Hence f and g are not inverses of each other.

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