Question

For f(x) = 8x +4 and g(x) = x?, find the following composite functions and state the domain of each. (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The domain of fog is {x (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain of fog is all real numbers. (b) (gof)(x) = (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The domain of g of is {x 1}. (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain of g of is all real numbers.

Answer 1

fin) = entu 2 { replace x with a numbers. (6) gof(") (replace ae with(8u+y) = quadratic - of tof(a) is set of all real numbers 1901 = x? ra) fog (2) f(g(u) = f(x) 8 (212)+4 fog(x) = 8x²+4 fog(x) is a quadrate function (an*+ butches form) and domain of a quadratic function is all real Option (B) is correct answer 9 (f(n)) =9 (8u+y) ( 8x+y)? g of (u) = Gun²+647+16 gof (x) is a function ( form an²+ brote) and domain of a quadratic function is all real numbers. Option (B) correct answer. (C) fof(x) f(f(n) = f( 8u+4) 818x+y)+4 replace with (8u+u) in f(u) = 640+36 The domain of a linear function is the set of all real numbers. (linear function äxtb) fof(u) is a linear function, ho, domain Option CB2 is correct answer (d) goglus 9 (9(x)) - 9(x2) {replace a with 2² in 9rxj] goging is a polynomial function and domain polynomial function is set of all real numbers. Option (B) is carrect answer ८- =(212) 2 24 a of