Question

$\text{A function}f:[-5,9]\to R$ is defined by :
$f\left(x\right)=\{\begin{array}{c}6x+1\text{if}-5\le x<2\\ 5x^2-1\text{if}2\le x<6\\ 3x-4\text{if}6\le x\le 9\end{array}$

Find $f\left(7\right)-f\left(1\right)$.

• A. 17
• B. 7
• C. 10
• D. 36

Answer 1

The correct option is C 10

$\text{Given,}f\left(x\right)=\{\begin{array}{c}6x+1\text{if}-5\le x<2\\ 5x^2-1\text{if}2\le x<6\\ 3x-4\text{if}6\le x\le 9\end{array}$
For a given value of x = a, find out the interval at which the point 'a' is located, there after find f (a) using the particular value defined in that interval.

Here, 7 lies in the 3rd interval. So for x = 7, $f\left(x\right)=3x-4$.
$\therefore f\left(7\right)=3\left(7\right)-4=17$

and 1 lies in the 1st interval. So, for x = 1, $f\left(x\right)=6x+1$
$\Rightarrow f\left(1\right)=6\left(1\right)+1=7$

$\therefore f\left(7\right)-f\left(1\right)=17-7=10$