Q55. - Algebra 2

Question

If $f\left(3a-1\right)=12a-7$, find $f\left(x\right)$.

Step-by-Step Solution

Answer

The required function is $f\left(x\right)=4x-3$.

Step 1 – Given information.

The given function is:

$f\left(3a-1\right)=12a-7$

To find the function $f\left(x\right)$.

Step 2 – Equate the input values.

$\begin{array}{l}3a-1=x\\ 3a=x+1\\ a=\frac{x+1}{3}\end{array}$

Step 3 – Substitute the value of the variable in the given function.

Substitute $a=\frac{x+1}{3}$ in the function $f\left(3a-1\right)=12a-7$.

$\begin{array}{l}f\left(3\left(\frac{x+1}{3}\right)-1\right)=12\left(\frac{x+1}{3}\right)-7\\ f\left(\left(x+1\right)-1\right)=4\left(x+1\right)-7\\ f\left(x+1-1\right)=4x+4-7\\ f\left(x\right)=4x-3\end{array}$

Thus, the required function is $f\left(x\right)=4x-3$.