Question

Escreva uma função f(x) = ax + b, sabendo que:

A) f(2) = 1/2 e f(4) = -2

B) a = 3 e f(3) = 5

C) a = 8 e b = 10

D) f(5)= -11 e f (10) = -14

Answer 1

a) f(2)= 2a+b
1/2= 2a+b
----------------
f(4)=4a+b
-2= 4a +b
------------------
2a+b=1/2
4a+b=-2x(-1)
---------------
2a+b= 1/2
-4a-b= 2
--------------
-2a= 1/2+2
-2a= 1+4/2
-2a=5/2
a=-5/2*1/2
a=-5/4
---------------
2a+b= 1/2
2(-5/4)+b= 1/2
-10/4+b= 1/2
-5/2+b= 1/2
b= 1/2+5/2
b= 6/2= 3
------------------------
f(x)= -5/4x+3
--------------------
b) a= 3
f(3)= 3a +b
5= 3*3+b
5= 9+b
5-9=b
b= -4
f(x) = 3x-4
--------------------
c) f(x)= ax+b
f(x)= 8x+10
----------------------
d) f(5)= 5a+b
-11= 5a+ b
5a+b= -11
f(10)= 10a+b
-14= 10a+b
---------------------
5a+b= -11 x(-1)
10a+b= -14
---------------
-5a-b= 11
10a+b= -14
---------------
5a= -3
a= -3/5
---------------
5(-3/5)+b= -11
-15/5+b= -11
-15+5b=-55
5b= -55+15
5b= -40
b= -40/5
b= -8
--------------------
f(x)= -3/5x-8

Answer 2

A)
f(x)= -5a/4 + 3

B)

f(x)= 5x/3

C)

f(x)=8x + 10

D)

f(x)= -3x/5 -8