Question

Given the tables for f & g below, find the following: x f ( x ) g ( x ) 0 9 7 1 4 8 2 3 6 3 5 1 4 7 5 5 1 2 6 6 0 7 0 4 8 2 9 9 8 3 Average rate of change of g for x on the interval [3 , 7 ] = 9 Incorrect Average rate of change of f for x on the interval [3 , 7 ] = Incorrect f ( g ( 4 ) ) = Incorrect g ( f ( 3 ) ) = Incorrect

Answer 1

$\\(i)\\ \text{We know that the average rate of change of a function f(x) on inerval [a,b] is}\\ \\ f_{avg}=\frac{f(b)-f(a)}{b-a}\\ \\ \text{so using this the average rate of chang of g for x on interval }[3,7] \text{ is}\\ \\ g_{avg}=\frac{g(7)-g(3)}{7-3}\\ \\ =\frac{4-1}{4}\\ \\ =\frac{3}{4}\\ \\ \text{so average rate of change of g on interval [3,7] is }\frac{3}{4}$

$\\(ii)\\ \text{Average rate of chang of f for x on interval }[3,7] \text{ is}\\ \\ f_{avg}=\frac{f(7)-f(3)}{7-3}\\ \\ =\frac{0-5}{4}\\ \\ =\frac{-5}{4}\\ \\ \text{so average rate of change of g on interval [3,7] is }\frac{-5}{4}$

$\\(iii)\\ \text{Since g(4)=5, so we have}\\ \\ f(g(4))=f(5)\\ \\ \text{since the value of f is 1 at x=5. so }\\ \\ f(g(4))=f(5)=1\\ \\ \text{hence we have, }f(g(4))=$ 1

$\\(iv)\\ \text{Since f(3)=5, so we have}\\ \\ g(f(3))=g(5)\\ \\ \text{since the value of g is 2 at x=5. so }\\ \\ g(f(3))=g(5)=2\\ \\ \text{hence we have, }g(f(3))=$ 2