Previous Problem Problem List Next Problem We discussed above how to find the domain of (fog)(z). To find the domain of

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Previous Problem Problem List Next Problem We Discussed Above How To Find The Domain Of Fog Z To Find The Domain Of 1 (34.95 KiB) Viewed 33 times

Previous Problem Problem List Next Problem We discussed above how to find the domain of (fog)(z). To find the domain of (gof)(x), we need to reverse the roles of f(x) and g(ar). We can calculate (gof)(2)-(f(x)), which is the evaluation of the function () for the input f(z), it (i) f(z) can be evaluated, that is, a is in the domain of f(z): the domain of f(x) consists of all real numbers, so there is no restriction here, and (ii) f() is in the domain of g(e), which is (-00,-10) (-10, 10) u (10,00). In order for f(ar) to belong to this interval, we must have (f(z)-10 and f(x) 10). (z-7-10 and 2-7/10) f) 7 - (2-3 and */17). Similarly, we can also check (8) by requiring the denominator of gf(r)) to be different from zero (z-7)²-1000 - Therefore the domain of (gof)(a) is (-00,-3) U(-3, 17)U(17,00). Note: To find the domain of a composition of functions, you must find the restrictions in (1) and (). The algebraic simplification not always gives the correct domain 1 25 ²142-510 - (x+3)(z-17) 0 Consider f(x)=z+5 and g(x)= . You must combine all like terms before you submit your answer. • You must expand all products before your submit your answer. a. Simplity: (fog)(x)= b. What is the domain of (fog)(x)? c. Simplity: (gof)(z)- d. What is the domain of (g)(x) Practice (2-3 and 2/17)