Download App

Functions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSFunctions4 Marks
Question
Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions: fg
✓

Answer

We have, $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ We observe that $\text{f(x)}=\sqrt{\text{x}+1}$ is defined for all $\text{x}\geq-1$ So, domain $\text{f}=[-1,\infty]$ Clearly, $\text{g(x)}=\sqrt{9-\text{x}^2}$ is defined for $9-\text{x}^2\geq0$ $\Rightarrow\text{x}^2-9\leq0$ $\Rightarrow\text{x}^2-3^2\leq0$ $\Rightarrow\text{x}\in[-3,3]$ $\therefore\ \text{domain(g)}=[-3,3]$ Now, $\text{domain(f)}\cap\text{domain(g)}$ $=[-1,\infty]\cap[-3,3]$ $=[-1,3]$ fg : [-1, 3] → R is given by (fg)(x) = f(x) × g(x) $=\sqrt{\text{x}+1}\times\sqrt{9-\text{x}^2}$ $=\sqrt{9+9\text{x}-\text{x}^2-\text{x}^3}$

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 "(Each question 4 marks)" from Functions→Functions — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Sketch the graphs of the following functions: $\text{f(x)}=\cot2\text{x}$
→
Convert the complex numbers given in Exercises in the polar form:
→
Evaluate the following limit: $\lim\limits_{\text{n}\rightarrow\infty}\frac{\sin\big(\frac{\text{a}}{2^{\text{n}}}\big)}{\sin\big(\frac{\text{b}}{2^{\text{n}}}\big)}$
→
Calculate the mean, variance and standard deviation of the following frequency distribution.
Class: 1-10 10-20 20-30 30-40 40-50 50-60
Frequency: 11 29 18 4 5 3
→
Find the mean deviation from the mean and from median of the following distribution:
Marks
0-10
10-20
20-30
30-40
40-50
No. of students
5
8
15
16
6
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{1}}\frac{1-\text{x}^2}{\sin\pi\text{ x}}$
→
Differentiate the following functions with respect to x:$\frac{\text{x}}{1+\tan\text{x}}$
→
Prove that:$\sin^2\text{B}=\sin^2\text{A}+\sin^2\text{(A}-\text{B)}-2\sin\text{A}\cos\text{B}\sin\text{(A}-\text{B)} $
→
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\frac{\sec\text{x}-1}{\sec\text{x+1}}$
→
If A, B, C are three sets such that $\text{A}\subset\text{B},$ then prove that $\text{C} - \text{B}\subset\text{C} - \text{A}.$
→