Question

sejam as funções f(x)= ax+b e g(x)=cx+d . sabendo-se que f(2)=3 , F(3)=5, G(2)=8 e g(3)=11 determine f(g(x))

Answer 1

f(x)= ax+b e g(x)=cx+d .

f(2)=3 , F(3)=5,

2a + b = 3(-1) 
3a + b = 5       ==> b = 5 - 3a==>b=5-3.(2)==> B=5-6 ==> B = - 1


-2a - b = -3 
3a + b = 5
  a = 2

f(x) = ax + b ==> f(x) = 2x - 1
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G(2)=8 e g(3)=11


2a + b = 8(-1) 
3a + b = 11       ==> b =11 - 3a==>b=11-3.(3)==> b =11-9 ==> b = 2


-2a - b = -8 
3a + b = 11
  a = 3

g(x) = ax + b ==> g(x) = 3x + 2 

determine f(g(x))


f(x) = 2x - 1
g(x) = 3x + 2 


f(g(x)) = 2(3x+2) - 1 ==> 6x + 4 - 1 ==> 6x + 3

Answer 2

Oi 

f(x) = ax + b

f(2) = 2a + b = 3
f(3) = 3a + b = 5

3a - 2a = 5 - 3
a = 2

4 + b = 3
b = -1

f(x) = 2x - 1

g(x) = ax + b

g(2) = 2a + b = 8
g(3) = 3a + b = 11

3a - 2a = 11 - 8
a = 3

6 + b = 8
b = 2

g(x) = 3x + 2

f(g(x)) = 2g(x) - 1

f(g(x)) = 2*(3x + 2) - 1 

f(g(x)) = 6x + 4 - 1 = 6x + 3

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