Q. 95.0( 2 Votes )

# 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.

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

Also, f(x) = 2x, and h(x) = ex

Now, f: N Zo 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.

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