A function f:[-5,9] R is defined as follow: f(x)= ll 6 x+1 ; & -5… - Vidyadip

Question

A function $f:[-5,9] \rightarrow R$ is defined as follow:
$f(x)=\left\{\begin{array}{ll}6 x+1 ; & -5 \leq x<2 \\5 x^2-1 ; & 2 \leq x<6 \\3 x-4 ; & 6 \leq x \leq 9\end{array} \text { Find } 2 f(4)+f(8)\right.$

✓

Answer

$f(x)=6 x+1 ; x=\{-5,-4,-3,-2,-1,0,1\}$
$f(x)=5 x^2-1 ; x=2,3,4,5$
$f(x)=3 x-4 ; x=\{6,7,8,9\}$
$2 f(4)+f(8)$
$f(x)=5 x^2-1$
$f(4)=5(4)^2-1=5(16)-1$
$=80-1=79$
$f(x)=3 x-4$
$f(8)=3(8)-4=24-4=20$
$2 f(4)+f(8)=2(79)+20$
$=158+20$
$=178$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[2 Mark Questions]" from Relations and Functions→Relations and Functions — all question types→MATHS STD 10 question papers→Tamilnadu Board STD 10 question papers→Tamilnadu Board question paper generator→

Similar questions

In the following case state whether the function is bijective or not. Justify your answer
f: R → R defined by f(x) = 2x + 1

Find the $10^{\text {th }}$ term of a G.P. whose $8^{\text {th }}$ term is 768 and the common ratio is 2

A building and a statue are in opposite side of a street from each other 35 m apart. From a point on the roof of building the angle of elevation of the top of statue is 24° and the angle of depression of base of the statue is 34°. Find the height of the statue. (tan 24° = 0.4452, tan 34° = 0.6745)

A box contains cards numbered 3, 5, 7, 9, … 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.

A hemispherical hollow bowl has material of volume cubic $\frac{436 \pi}{3}$ cubic $cm$. Its external diameter is 14 $cm$. Find its thickness

In a two children family, find the probability that there is at least one girl in a family

The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm$^2$

Let $f ( x )=2 x +5$. If $x \neq 0$ then find $\frac{f(x+2)- f (2)}{r}$

Check whether the following sequence is in A.P.
1, –1, 1, –1, 1, –1, …

In the matrix $A=\left[\begin{array}{cccc}8 & 9 & 4 & 3 \\ -1 & \sqrt{7} & \frac{\sqrt{3}}{2} & 5 \\ 1 & 4 & 3 & 0 \\ 6 & 8 & -11 & 1\end{array}\right]$, write The number of elements