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 the value of $f\left(6\right)$.

• A. 14
• B. 179
• C. 37
• D. 2

Answer 1

The correct option is A 14

$\text{Given,}f\left(x\right)=\{\begin{array}{c}6x+1\text{if}-5\le x<2\\ 5x^2-1\text{if}2\le x<6\\ 3x-4\text{if}6\le x\le 9\end{array}$
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, 6 lies in the 3rd interval. So for x = 6, $f\left(x\right)=3x-4$.
$\therefore f\left(6\right)=3\left(6\right)-4=14$