Mathematics: Given that f left parenthesis x right parenthesis equal 3 x minus 5 and that 3 f left parenthesis a right parenthesis equal f left parenthesis 2 a plus 1 right parenthesis , determine the value for a .

-2/3Step-by-step explanation:...

Given that f left parenthesis x right parenthesis

shreyasvrangan

02.01.2022

The value of a is $a=\frac{13}{3}$ .

Step-by-step explanation:

Given function is

f(x)=3x-5

It is given that

3f(a)=f(2a+1) .... (1)

We need to find the value of a.

Substitute x=a in the given function.

f(a)=3a-5 .... (2)

Substitute x=(2a+1) in the given function.

f(2a+1)=3(2a+1)-5

f(2a+1)=6a+3-5

f(2a+1)=6a-2 .... (3)

Substitute value of f(a) and f(2a+1) in equation (1) from (2) and (3).

3(3a-5)=6a-2

9a-15=6a-2

Separating the variable, we get

9a-6a=15-2

3a=13

Divide both sides by 3.

$a=\frac{13}{3}$

Therefore the value of a is $a=\frac{13}{3}$ .

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