Question

Let $f\left(x\right)=ax+b$ and $f\left(6\right)-f\left(2\right)=12$ then $f\left(2\right)-f\left(1\right)$ is

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is A $3$

$f\left(x\right)=ax+b$

$f\left(6\right)=6a+b$ ____ (1)

$f\left(2\right)=2a+b$ ____ (2)

eq (1) - eq (2)

$f\left(6\right)-f\left(2\right)=6a+b-2a-b=4a=12$. given

$\Rightarrow a=3$

$f\left(2\right)=2a+b$

$=2\times 3+b$

$f\left(2\right)=6+b$ ____ (3)

$f\left(1\right)=a+b$

= $3+b$ _____ (4)

$f\left(2\right)-f\left(1\right)=6+b-3-b=3$