Download App

Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions3 Marks
Question
Check if the following functions have an inverse function. If yes, find the inverse function.

$f(x)=\sqrt{4 x+5}$

✓

Answer

$\mathrm{f}(\mathrm{x})=\sqrt{4 x+5}, x \geq \frac{-5}{4}$
Let $\mathrm{f}\left(\mathrm{x}_1\right)=\mathrm{f}\left(\mathrm{x}_2\right)$
$\therefore \sqrt{4 x_1+5}=\sqrt{4 x_2+5}$
$\therefore \mathrm{x}_1=\mathrm{x}_2$
$\therefore \mathrm{f}$ is a one-one function.
$\mathrm{f}(\mathrm{x})=\sqrt{4 x+5}=\mathrm{y}$, (say) $\mathrm{y} \geq 0$
Squaring on both sides, we get
$\mathrm{y}^2=4 \mathrm{x}+5$
$\therefore \mathrm{x}=\frac{y^2-5}{4}$
$\therefore$ For every y we can get $\mathrm{x}$.
$\therefore \mathrm{f}$ is an onto function.
$\therefore \mathrm{x}=\frac{y^2-5}{4}=\mathrm{f}^{-1}(\mathrm{y})$
Replacing y by $x$, we get
$f^{-1}(x)=\frac{x^2-5}{4}$

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 "Solve the Following Question.(3 Marks)" from Functions→Functions — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
→
If $a, b, c$ are in G.P., prove that:
$\frac{(\text{a}+\text{b}+\text{c})^2}{\text{a}^2+\text{b}^2+\text{c}^2}=\frac{\text{a}+\text{b}+\text{c}}{\text{a}-\text{b}+\text{c}}$
→
Find the equation of line which passes through the point of intersection of lines $3 x+2 y-6=0, \quad x+y+1=0$ and the point $\mathrm{A}(2,1)$.
→
Differentiate the following w.r.t. x :y = ex tan x + cos x log x – √x 5x
→
Show the following quadratic equation by factorization method:
$\text{x}^2+\frac{\text{x}}{\sqrt{2}}+1=0$
→
If e and e’ are the eccentricities of a hyperbola and its conjugate hyperbola respectively,prove that $\frac{1}{e^2}+\frac{1}{\left(e^{\prime}\right)^2}=1$.
→
Solve the following quadratic equations:

$2 x^2+3 i x+2=0$

→
Calculate the coefficient of variation of the following data.

23, 27, 25, 28, 21, 14, 16, 12, 18, 16

→
Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{4}}\left[\frac{\tan ^2 x-\cot ^2 x}{\sec x-\operatorname{cosec} x}\right]$
→
Find the rational number having the following decimal expansions:$0.\overline{3}$
→