In Example 10, f and g are both linear. 

(a) Find symbolic representations for f and g. 

(b) Determine (g ° f)(x). 

(c) Evaluate (g ° f) (3.5) and interpret the result.

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EXAMPLE 10 Evaluating a composite function numerically Depletion of the ozone layer can cause an increase in the amount of UV radiation reaching the surface of Earth. An increase in UV radiation is associated with skin cancer. In TABLE 5.4 the function f computes the approximate percent increase in UV radiation resulting from an x percent decrease in the thickness of the ozone layer. The function g shown in TABLE 5.5 computes the expected percent increase in cases of skin cancer resulting from an x percent increase in UV radiation. (Source: R. Turner, D. Pearce, and I. Bateman, Environmental Economics.) X f(x) TABLE 5.4 x TABLE 5.5 0 0 0 0 Percent Increase in UV Radiation 1 2 3 1.5 3.0 4.5 4 6.0 5 7.5 6 9.0 Percent Increase in Skin Cancer 1.5 3.0 4.5 6.0 7.5 9.0 5.25 10.5 15.75 21.0 26.25 31.5 (a) Find (gof)(2) and interpret this calculation. (b) Create a table for gof. Describe what (gof)(x) computes. Percent decrease in the ozone layer Percent increase in UV radiation Percent increase in UV radiation Percent increase in cases of skin cancer