Question

Find fog and go f. f(x) = Vx+4, g(x) = x2 (a) fog (b) gof x +4 Find the domain of each function and each composite function. domain off domain of g domain of fog domain of g of

Answer 1

The given functions are f(x) = 5x+4 g(x) = x² (a) fog f(g(x)) f (x²) [: g(x) = x² = x² + 4 (putting x= x² in fro] fog = 5 x ²44 (b) got gCf(x)) f(x) = √x+4 (1249) LFC (der)" spurting x= x 44 in 90 x + 9 11 .: got x +4 7 The domain of a function is the set of values that that the function can take as its input. • Here given. f(x) = √x+4 if x+470 We that f(x) is defined if xY 4 je, if so of input which real numbers as its can take any greaten or equal to 4

Therefore the domain of f is - the set of [{XER: XY-4} where it is all real numbens. g(x) = x² we Giren that g(x) see that gex) is defined for all e the domain of 'g is all real number. il the domain of ins 00 2: x t IR 2 IR is the set of all seal numbers we have, fog V x²+4 Herle 'g' defined for all a, as well as 'fog' is defined for all e. 80, the domain of fog X: x t IR where IR is the set of all real numbers, We have, X+ 4 is defined for all x y - 4 got Here of and We see that that gif is defined for all x.

this two we the domain so, combin get, mbining of fog is XER: 2 - 4 Where IR is the set of all real number Answer: (a) tog Wx²+4 시 (b) gof x+4 domain of at XEIR: xY-4} -4} domain of ob X: REIRY X: xt IR domain of fog domain of gof XEIR: x²-47