What is the inverse function of the following functions a f

What is the inverse function of the following functions?

a. f : N N-{0, 1} f (m) = m + 2

b. g : R R g(x) = 2x 3 7.

a) Let the function f(m) = y

y = m + 2

y - 2 = m

replace m and y we get

y = m - 2

Hence the inverse function g(m) = m-2

Proof: If the function f and g are inverse of each other, then f(g(m)) = m and g(f(m)) = m

f(g(m)) = f(m-2) = (m-2) + 2 = m

g(f(m)) = g(m+2) = (m-2) + 2 = m

Hence the function f and g are inverse of each other

b) Let the function g(x) = y

y = 2x^3 - 7

y + 7 = 2x^3

x^3 = (y+7)/2

x = [(y+7)/2]^(1/3)

Replace x and y we get

y = f(x) = [(x+7)/2]^(1/3)

Proof: If the function f and g are inverse of each other, then f(g(x)) = x and g(f(x)) = x

f(g(x)) = f([(x+7)/2]^(1/3)] = 2(x+7)/2 - 7 = x + 7 - 7 = x

g(f(x)) = f(2x^3 - 7) = x

Hence the f and g are inverse of one another