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Two functions f(x) and g(x) are inverse of each other if f(g(x)) = g(f(x)). Let us see in each of the cases if this holds true or not.

Part (a):

We are given f(x) = 6x and g(x) = 6x

So f(g(x)) = 6(6x) = 36x

and g(f(x)) = 6(6x) = 36x

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

Hence f and g are inverse of each other.

Part (b):

We are given f(x) = 2x-7 and g(x) = (x+7)/2

So f(g(x) = f((x+7)/2)

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

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

f(g(x)) = x

Now g(f(x)) = g(2x-7)

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

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

g(f(x)) = x

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