Question

Let $f$ be a linear function for which $f\left(6\right)-f\left(2\right)=12$. The value of $f\left(12\right)-f\left(2\right)$ is equal the

• A. $12$
• B. $18$
• C. $24$
• D. $30$

Answer 1

The correct option is D $30$

Let $f\left(x\right)=ax+b$ [Since $f$ is given to be linear function] where $a$ and $b$ are constants.

According to the problem

$f\left(6\right)-f\left(2\right)=12$

or, $6a-b-2a-b=12$

or, $4a=12$

or, $a=3$.

Now

$f\left(12\right)-f\left(2\right)$

$=12a+b-2a-b$

$=10a=30$. [Using value of $a$]