What is the range of the function h(x) = frac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To find the range of the function $h(x) = \frac{x-2}{x+3}$,let $h(x) = y$.Set $y = \frac{x-2}{x+3}$.Multiply both sides by $(x+3)$:$y(x+3) = x-2$$

Vedclass · Accepted Answer

$(-\infty, 1) \cup (1, \infty)$

Vedclass · Answer

(B) To find the range of the function $h(x) = \frac{x-2}{x+3}$,let $h(x) = y$.Set $y = \frac{x-2}{x+3}$.Multiply both sides by $(x+3)$:$y(x+3) = x-2$$xy + 3y = x - 2$Rearrange to solve for $x$:$xy - x = -3y - 2$$x(y-1) = -(3y + 2)$$x = \frac{-(3y+2)}{y-1} = \frac{3y+2}{1-y}$.For $x$ to be defined,the denominator $1-y 
eq 0$,which means $y 
eq 1$.Thus,the range of the function is all real numbers except $1$,which is $(-\infty, 1) \cup (1, \infty)$.

What is the range of the function $h(x) = \frac{x-2}{x+3}$?

Similar Questions

Is it true that $x = e^{\log x}$ for all real $x$?

The domain of $f(x) = \sqrt{\log_2\left(\frac{10x - 4}{4 - x^2}\right) - 1}$ is

If $[x]$ denotes the greatest integer $\leq x$, then the range of the real-valued function $f(x) = \frac{1}{\sqrt{x-[x]}}$ is

The domain of the real-valued function $f(x) = \sqrt{\frac{2-|x|}{3-|x|}}$ is

The function is defined as $f(x) = (1 + \frac{1}{x})^x$. What is the range of the function $f(x)$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module