Verify associativity for the following three mappings: f: N → Z₀ (the set of non – zero integers), g: Z₀→ Q and h: Q → R given by f(x) = 2x, g(x) = 1/x and h(x) = e^x.

Question

Verify associativity for the following three mappings: f: N → Z 0 (the set of non – zero integers), g: Z 0 → Q and h: Q → R given by f(x) = 2x, g(x) = 1/x and h(x) = e x .

Philoid · Accepted Answer

We have, f: N → Z_o, g: Z₀ → Q and h: Q → R

Also, f(x) = 2x, and h(x) = e^x

Now, f: N → Z_o and hog: Z₀ → R

∴ (hog)of: N → R

Also, gof: N → Q and h: Q → R

∴ ho(gof): N → R

Thus, (hog)of and ho(gof) exist and are function from N to set R.

Finally. (hog)of(x) = (hog)(f(x)) = (hog)(2x)

Now, ho(gof)(x) = ho(g(2x)) = h

Hence, associativity verified.

Verify associativity for the following three mappings: f: N → Z0 (the set of non – zero integers), g: Z0→ Q and h: Q → R given by f(x) = 2x, g(x) = 1/x and h(x) = ex.

Verify associativity for the following three mappings: f: N → Z₀ (the set of non – zero integers), g: Z₀→ Q and h: Q → R given by f(x) = 2x, g(x) = 1/x and h(x) = e^x.