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

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

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

5 0

4 years ago

to solve the following equation , 7x - 2 = 12 , which of the choices below is a correct method to find the value of X￼￼￼

to solve the following equation , 7x - 2 = 12 , which of the choices below is a correct method to find the value of X