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Example 2 Find each of the following functions, and state its domain. (a) Ro ( QoP )

Example 2 Find each of the following functions, and state its domain. (a) Ro ( QoP ) Solution (a) The composite function ( QoP )( x ) is obtained by substituting P(x) for x in the formula of Q(x) . Now the formula for ( Ro ( QoP ))( x ) is obtained by substituting ( QoP )( x ) for

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Example 2 Find each of the following functions, and state its domain. (a) Ro ( QoP )

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  1. Example 2 Find each of the following functions, and state its domain. (a) Ro(QoP) Solution(a) The composite function (QoP)(x) is obtained by substituting P(x) for x in the formula of Q(x). Now the formula for (Ro(QoP))(x) is obtained by substituting (QoP)(x) for x in the formula for R(x). The domain of Ro(QoP) is the domain of QoP which is the domain of P which is the set .

  2. (b) (RoQ)oP The composite function (RoQ)(x) is obtained by substituting Q(x) for x in the formula of R(x). Now the formula for ((RoQ)oP)(x) is obtained by substituting P(x) for x in the formula for (RoQ)(x). The domain of (RoQ)oP is the domain of P which is the set . Observe that Ro(QoP) and (RoQ)oP are the same function – they have the same formula and the same domain. Hence we denote this function as RoQoP, omitting the parentheses. Note that the range of RoQoP is [2,) which is a proper subset of the range [0,) of R.

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