Question

Please answer these questions *clearly*

Answer 1

1.
f(x ) = { x² , 0 ≤ x ≤ 3
= {3x , 3 ≤ x ≤ 10

we know that , any expression will be function only when , there is only one value gain of dependent variable with respect to independent variable.

see here f(x) = x² when , 0 ≤ x ≤ 3
if we take x = 3 then y = (3)² = 9
hence, one value of x , we get one value of f(x) .

again , f(x) = 3x when, 3 ≤ x ≤ 10
if we take x = 3 then y = 3(3) = 9
here also if we take one value of x {e.g x = 3 } we get only one value of f(x).{e.g f(x ) = 9 }

hence f(x) is function .

/
g(x) = { x² 0 ≤ x ≤ 2
= { 3x , 2 ≤ x ≤ 10

g(x) = x² when, 0 ≤ x ≤ 2
take x = 2 then , f(x) = (2)² = 4

again, g(x) = 3x when , 2 ≤ x ≤ 10
take x = 2 then, f(x) = 3(2) = 6

here you can see that one value of x {e.g x = 2 } we get two value of g(x) { e.g 4 , 6 } hence, g(x) is not satisfying of function condition.
hence, g(x) isnt a function .




2.
f(x) = x²

then, { f(1.1) - f(1) }/(1.1 - 1)

f(1.1) = (1.1)² = 1.21
f(1) = 1

put it ,

= { 1.21 - 1}/(1.1 - 1)

= { 0.21 }/(0.1)

= 2.1

Answer 2

i hope this will help you