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 $f\left(4\right)+f\left(8\right)$.

• A. 99
• B. 79
• C. 24
• D. 199

Answer 1

The correct option is A 99

$\text{Given,}f\left(x\right)=\{\begin{array}{c}6x+1\text{if}-5\le x<2\\ 5x^2-1\text{if}2\le x<6\\ 3x-4\text{if}6\le x\le 9\end{array}$
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, 4 lies in the 2nd interval. So for x = 4, $f\left(x\right)=5x^2-1$.
$\therefore f\left(4\right)=5\left(4^2\right)-1=79$

and 8 lies in the 3rd interval. So, for x = 8, $f\left(x\right)=3x-4$
$\Rightarrow f\left(8\right)=3\left(8\right)-4=20$

$\therefore f\left(4\right)+f\left(8\right)=79+20=99$