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 1. relation and function→1. relation and function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$f(x)=x^x$ has a stationary point at

A fair die is tossed eight times. The probability that a third six is observed in the eight throw is:

$\frac{\text{ }^7\text{C}_2\times5^5}{6^7}$
$\frac{\text{ }^7\text{C}_2\times5^5}{6^8}$
$\frac{\text{ }^7\text{C}_2\times5^5}{6^6}$
$\text{None of these}$

Let $f$ be a function such that $f(x)\, = \,\sum\limits_{n\, - \,1}^n {\left[ {r\, + \,\cos \frac{x}{r}} \right]} $ where [.] denotes greatest integer function and $x \in [0,\pi]$, then range of $f(x)$ is-

If a system of the equation ${(\alpha + 1)^3}x + {(\alpha + 2)^3}y - {(\alpha + 3)^3} = 0$ and $(\alpha + 1)x + (\alpha + 2)y - (\alpha + 3) = 0,x + y - 1 = 0$ is constant. what is the value of $\alpha $

If $f(x) = \left\{ \begin{array}{l}{(1 + 2x)^{1/x}},\,{\rm{for\,\, }}x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{e^2},\,{\rm{for\,\, }}x = 0\,\,\,\end{array} \right.$, then

If $2x = {y^{\frac{1}{5}}} + {y^{ - \frac{1}{5}}}$ and $(x^2 -1) \frac{{{d^2}y}}{{d{x^2}}} + \lambda x\frac{{dy}}{{dx}} + ky = 0$ , then $ \lambda + k$ is equal to

Let $\begin{vmatrix}\text{x}^2+3\text{x}&\text{x}-1&\text{x}+ 3\\\text{x}+1&-2\text{x}&\text{x}-4\\\text{x}-3&\text{x}+4&3\text{x}\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}$ be an identity in x, where a, b, c, d, e are independent of x. Then the value of e is:

4
0
1
None of these.

Let $[\mathrm{t}]$ denote the greatest integer $\leq \mathrm{t}$. Then the value of $8 \cdot \int \limits_{-\frac{1}{2}}^{1}([2 x]+|x|) \,d x$ is .... .

Choose the correct answer from the given four options.
The angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ with magnitudes $\sqrt{3}$ and 4, respectively, and $\vec{\text{a}}\cdot\vec{\text{b}}=2\sqrt{3}$ is:

$\frac{\pi}{6}$
$\frac{\pi}{3}$
$\frac{\pi}{2}$
$\frac{5\pi}{2}$

The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:

$\frac{5}{3\sqrt{3}}$
$\frac{10}{3\sqrt{3}}$
$\frac{25}{3\sqrt{3}}$
$\text{None of these}$