Name: Properties of Binary Operations
Uploaded: 2019-07-19
Duration: 12 min 41 s
Description: In this video, we will learn about binary operations. We will also understand properties followed by binary operations with the help of suitable examples.

Question

Consider a bijective function

f : R_{+} \to (7, \infty)

given by

f (x) = 16 x^{2} + 24 x + 7

, where

R_{+}

the set of all positive real numbers. Find the inverse function of

f

.

Accepted Answer

Given that, $f : R_{+} \to (7, \infty)$ is a bijective function.

Therefore, the inverse of the function exists.

Now, $f (x) = 16 x^{2} + 24 x + 7$

Let $y = f^{- 1} (x)$

$\Rightarrow f (y) = x$

$\Rightarrow 16 y^{2} + 24 y + 7 = x$

$\Rightarrow 16 y^{2} + 24 y + (7 - x) = 0$

$\Rightarrow y = \frac{- 24 \pm \sqrt{576 - 4 (16) (7 - x)}}{32}$

$\Rightarrow y = \frac{- 24 \pm \sqrt{576 - 448 + 64 x}}{32}$

$\Rightarrow y = \frac{- 24 \pm \sqrt{128 + 64 x}}{32}$

$\Rightarrow y = \frac{- 24 \pm 8 \sqrt{2 + x}}{32}$

$\Rightarrow y = \frac{- 3 \pm \sqrt{2 + x}}{4}$

As $y \in R_{+}$ , so $y$ cannot be negative.

Therefore, $y = \frac{- 3 + \sqrt{2 + x}}{4}$

Hence, $f^{- 1} (x) = \frac{- 3 + \sqrt{2 + x}}{4}$

Consider a bijective function $f : R_{+} \to (7, \infty)$ given by $f (x) = 16 x^{2} + 24 x + 7$ , where $R_{+}$ the set of all positive real numbers. Find the inverse function of $f$ .

Important Questions on Relations and Functions

Learn and Prepare for any exam you want !

Consider a bijective function f:R+→(7,∞) given by f(x)=16x2+24x+7, where R+ the set of all positive real numbers. Find the inverse function of f.

Important Questions on Relations and Functions

Learn and Prepare for any exam you want !

Consider a bijective function $f : R_{+} \to (7, \infty)$ given by $f (x) = 16 x^{2} + 24 x + 7$ , where $R_{+}$ the set of all positive real numbers. Find the inverse function of $f$ .