4. Let f(x) = 3x – 5 and g(x) = 2×2 +1. Find: a. (gºf)(x) b. f'(x) 5. Graph and determine the domain and range of each function. a. y = 3* b. y = log;*

## Answer

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f(n)= 32-5 a) (gof)(x) gex) = 2x²+2 9 (+(x)) 2(3-5) 2+1 2(9x*+ 25 – 30n) + 1 18n²+ 50 – 60x + 1 18r2a-600 +51 (Aus) get b) fo(a) can be f(x) = y = 3x – 5 – 3- y +5 -) = [let f(a) be y y +5 3 CS —- [We exchange y with x in the end +5 3 5-‘(w is! 5 be se to 2 the graph can y = 32 (ارہ) 1 3 1 92 the from this On logx. we com say, domain is all real numbers i. & R and Range [as all the values of y] (0,00) (Au) b) ya the graph can be, log3 1 2 log x=0 (3 (3.1) (10) 13 o 2 x=1

As only positive side of gaasis is taken (ie. positive xe) so the domain of the function is (0, 0) (Aus) From the graph we can sag the na of the function range is set of all Real numbers ie R. (Aus)