State True or False for the statements. The composition of functi… - Vidyadip

Question

State True or False for the statements.
The composition of functions is associative.

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Answer

True.Solution:
Let us suppose f(x) = x, g(x) = x + 1 and h(x) = 2x - 1
Now, fo{goh(x)} = f[g{h(x)}]
= f{g(2x - 1)} $[\because$ h(x) = 2x - 1$]$
= f(2x - 1 + 1)
f(2x) = 2x
Also, (fog)oh(x) = (fog){h(x)}
= (fog)(2x - 1)
= f{g(2x - 1)}
= f(2x - 1 + 1)
= f(2x) = 2x

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