Respuesta :
Answer:
The value of a is [tex]a=\frac{13}{3}[/tex].
Step-by-step explanation:
Given function is
[tex]f(x)=3x-5[/tex]
It is given that
[tex]3f(a)=f(2a+1)[/tex] .... (1)
We need to find the value of a.
Substitute x=a in the given function.
[tex]f(a)=3a-5[/tex] .... (2)
Substitute x=(2a+1) in the given function.
[tex]f(2a+1)=3(2a+1)-5[/tex]
[tex]f(2a+1)=6a+3-5[/tex]
[tex]f(2a+1)=6a-2[/tex] .... (3)
Substitute value of f(a) and f(2a+1) in equation (1) from (2) and (3).
[tex]3(3a-5)=6a-2[/tex]
[tex]9a-15=6a-2[/tex]
Separating the variable, we get
[tex]9a-6a=15-2[/tex]
[tex]3a=13[/tex]
Divide both sides by 3.
[tex]a=\frac{13}{3}[/tex]
Therefore the value of a is [tex]a=\frac{13}{3}[/tex].
