If f(x)= ll x+a, & x 0 |x-4|, & x>0 . and g(x)= ll x+1 & x<0 (x-4… - Vidyadip

MCQ

If $f(x)=\left\{\begin{array}{ll}x+a, & x \leq 0 \\ |x-4|, & x>0\end{array}\right.$ and $g(x)=\left\{\begin{array}{ll}x+1 & x<0 \\ (x-4)^{2}+b, & x \geq 0\end{array}\right.$ are continuous on $R$, then $(gof) (2)+( fog) (-2)$ is equal to.

A
$-10$
B
$10$
C
$8$
✓
$-8$

✓

Answer

Correct option: D.

$-8$

d
$(x)=\left\{\begin{array}{l} x+a ; x \leq 0 \\ |x-4| ; x>0 \end{array} ; g(x)=\left\{\begin{array}{ll} x+1 & ; x<0 \\ (x-4)^{2}+b ; & x \geq 0 \end{array}\right.\right.$

For continuity $a =4$ and $b =-15$

$g(f(2))+f(g(-2))$

$=g(2)+f(-1)=-8$

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 "M.C.Q (1 Marks)" from STD 12 - 1. relation and function→STD 12 - 1. relation and function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The value of $\int {\frac{{{e^x}\, + \,9\,\cos \,x\, - \,2\,\sin \,x\, + \,7}}{{{e^x}\, + \,7\,\sin \,x\, + \,11\,\cos \,x\, + \,14}}\,dx} $ is

(where $C$ is constant of integration)

Let $X$ be a discrete random variable. Then the variance of $X$ is :

If $f(x) = \left\{ \begin{array}{l}1 + x,\;{\rm{when\,\, }}x \le 2\\5 - x,\,{\rm{when \,\,}}\,x \le 3\end{array} \right.$, then

Let $A$ be a square matrix of order $2$ such that $|A|=2$ and the sum of its diagonal elements is $-3$ . If the points $(x, y)$ satisfying $A^2+x A+y I=0$ lie on a hyperbola, whose transverse axis is parallel to the x-axis, eccentricity is e and the length of the latus rectum is $\ell$, then $\mathrm{e}^4+\ell^4$ is equal to...........................

${\tan ^{ - 1}}\frac{{a - b}}{{1 + ab}} + {\tan ^{ - 1}}\frac{{b - c}}{{1 + bc}} = $

If $A=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ two matrix, then find AB ?

If matrix $A = \left[ {\begin{array}{*{20}{c}}3&2&4\\1&2&{ - 1}\\0&1&1\end{array}} \right]$and ${A^{ - 1}} = \frac{1}{K}adj(A),$ then $K$is

Let $X$ and $Y$ be two events such that $P(X \mid Y)=\frac{1}{2}, P(Y \mid X)=\frac{1}{3}$ and $P(X \cap Y)=\frac{1}{6}$. Which of the following is (are) correct?

$(A)$ $P(X \cup Y)=\frac{2}{3}$

$(B)$ $X$ and $Y$ are independent

$(C)$ $X$ and $Y$ are not independent

$(D)$ $P\left(X^C \cap Y\right)=\frac{1}{3}$

$2x + 3y + 4z = 9$,$4x + 9y + 3z = 10,$$5x + 10y + 5z = 11$ then the value of $ x$ is

${\cos ^{ - 1}}\left( {\frac{{3 + 5\cos x}}{{5 + 3\cos x}}} \right)$ is equal to