Question

Find the value of $f\left(2x\right),2f\left(x\right)$for the function $f\left(x\right)=3x-1$.

Short answer

The value of $f\left(2x\right)=6x-1\text{and}2f\left(x\right)=6x-2$.

Step-by-step solution

Step 1. Evaluate f2x for the function.

From the given function,

$f\left(x\right)=3x-1....\left(1\right)$

Evaluate the value of function at $x=2x$gives,

localid="1644526114050" $$\begin{gathered} f\left(2x\right)=3\left(2x\right)-1....\left(\text{Substitute}x=2x\text{in}\left(1\right)\right) \\ =6x-1 \end{gathered}$$

Step 2. Similarly evaluate 2fx the function.

Similarly, evaluate $2f\left(x\right)$for the function,

localid="1644526093803" $$\begin{gathered} 2f\left(x\right)=2\left(3\left(x\right)-1\right)\mathrm{....}\left(\text{Multiply}\left(1\right)\text{by2}\right) \\ =6x-2 \end{gathered}$$

Step 3. Description of steps.

From the obtained values $f\left(2x\right)=6x-1\text{and}2f\left(x\right)=6x-2$.