Mathematics: Equation Problem................................

1
Question 1
Given equation
f(x) = - 4x
2
+ 3x – 5
a) f (3) = ?
f(x) = - 4x
2
+ 3x – 5
f (3) = - 4.(3)
2
+ 3.(3) – 5
= -36+ 9-5
=-32
b) f(-2x) + 5 f(x) = ?
f(x) = - 4x
2
+ 3x – 5
f(-2x) = - 4 .( -2x)
2
+ 3(-2x) – 5
= -4(4 x
2
) -6x -5
= -16 x
2
-6x-5
5f(x) = 5. (- 4x
2
+ 3x – 5)
= -20 x
2
+15x – 25
Now,
2

f(-2x) + 5 f(x) =( -16 x
2
-6x-5 ) + (-20 x
2
+15x – 25 )
= -16 x
2
– 6x – 5 - 20 x
2
+15 x – 25
= - 36 x
2
+ 9x – 30
c)
( ) ( )

= ?
( ) - 4x2 + 3x – 5
( ) - 4(a)2 + 3.(a) – 5 = - 4 a2 + 3a - 5
Now,
( ) ( )


( ) ( )


=



=
( ) ( )


=
( ) ( )


=
( ) ( ) ( )


Identity = ( ) ( )( )
=
( )*( ( )) +
( )

= -4(x +a) +3
= -4x-4a+3
3

Question 2
Given equation
f(x) = 3x
2
...