Expressing x in Terms of y, to Find the Range of a Function

Q.

The range of the function $f\left(x\right)=\frac{x^2-x}{x^2+2x}$ is

1. $R-\left\{1\right\}$

2. $R-\{-\frac{1}{2},1\}$

3. None of these

4. $R$

Q. The number of integers in the range of $f\left(x\right)={\sec }^{-1}(9x^2+6x-1)$ is

1. $3$
2. $4$
3. $1$
4. $2$

Q. $Therangeof{x}^2+4y^2+9z^2-6yz-3xz-2xyis$

1. 
2. 
3. 
4. R

Q. The range of the function $f\left(x\right)=\frac{2+x}{2-x},x\ne 2$ is

1. $R$
2. $R-\{-1\}$
3. $R-\left\{1\right\}$
4. $R-\{-2\}$

Q. $f\left(x\right)=\frac{x^2-3x+4}{x^2+3x+4}$ the range of f(x) is

1. $(-\infty ,\frac{1}{7})\cup (7,\infty )$
2. $[\frac{1}{7},7]$
3. $[0,\frac{1}{7}]$
4. $(-\infty ,7)$

Q. The solution of

Q.

Let $f:R^{+}\to R$, where $R^{+}$ is the set of all positive real numbers, be such that $f\left(x\right)=lo{g}_{e}x$, Determine
i) The image set of the domain of f
ii) $\{x:f(x)=-2\}$
iii) Whether $f\left(xy\right)=f\left(x\right)+f\left(y\right)$ holds.

Q.

The range of the function $f\left(x\right)=\frac{x}{|x|}$ is

1. R - {0}

2. R - {-1, 1}

3. {-1, 1}

4. None of these

Q.

If x is real and k =$\frac{x^2-x+1}{x^2+x+1}$, then

1. $k\in [\frac{1}{3},3]$

2. $k\le \frac{1}{3}$

3. $k\ge 3$

4. none of these

Q. The range of the function $f\left(x\right)=\frac{2+x}{2-x},x\ne 2$ is

1. $R-\left\{1\right\}$
2. $R-\{-2\}$
3. $R$
4. $R-\{-1\}$

Q. lf $xy=e-e^y$ then $\frac{d^{2}y}{d{x}^2}$, when $x=0$, is equal to

1. $\frac{1}{e}$
2. $\frac{1}{e^3}$
3. $\frac{1}{e^2}$
4. $0$

Q. Let $f:R\to R$ be a function defined by $f\left(x\right)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$ then

1. $f$ is an injection only
2. $f$ is a bijection
3. $f$ is a surjection
4. $f$ is neither an injection nor a surjection

Q. If $x,y,z$ are real numbers such that $x+y+z=4$ and $x^2+y^2+z^2=6,$ then the range of $x$ is

1. $(-1,1)$
2. $[0,2]$
3. $[\frac{2}{3},2]$
4. $[2,3]$

Q. $Therangeofthefunctionf\left(x\right)=\frac{2+x}{2-x},x\ne 2is$

1. 
   R-{1}
2. R-{2}
3. R
4. R-{-1}

Q. Range of the function $y=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is

1. $(-1,1)$
2. $[-1,1]$
3. $R$
4. $(0,1)$

Q. Find the values of $x$ and $y$. If ${\log }_{10}(x-1)={\log }_{10}(y+4)$ and $x+y=6$.

Q.

The range of f(x) = $\frac{x^2+x+1}{x^2+x-1}$

1. $(-\infty ,\frac{-3}{5}]\bigcup [1,\infty )$

2. $(-\infty ,\frac{-3}{5}]\bigcup (1,\infty )$

3. $(-\infty ,\frac{3}{5})\bigcup (1,\infty )$

4. $(-\infty ,\frac{5}{3}]\bigcup [2,\infty )$

Q. Find the points at which the function $f$ given by $f\left(x\right)={(x-2)}^4{(x+1)}^3$ has local maxima

Q.

If $y=f\left(x\right)=\frac{ax-b}{bx-a}$, show that $x=f\left(y\right)$.

Q.

The range of f(x) = $\frac{x^2+x+1}{x^2+x-1}$

1. (-∞ , -3/5 ] U (1, ∞)

2. (-∞ , -3/5 ) U (1, ∞)

3. (-∞ , -3/5 ] U [1, ∞)

4. None of these

Q. The range of the function f(x) $=\frac{x-2}{2-x}$ when x $\ne$ 2 is

1. R
2. R - {1}
3. {-1}
4. R-{-1}

Q. The range of the function $f\left(x\right)=\frac{x+2}{|x+2|}$ is

Q. The range of the function f(x) $=\frac{x-2}{2-x}$ when x $\ne$ 2 is

1. R
2. R - {1}
3. {-1}
4. R-{-1}

Q. Find the sum of the digits of the value of $y\left(\log 4\right)$ if $y_2-7y_1+12y=0,y\left(0\right)=2,y_1\left(0\right)=7$.

Q. Range of the function $y=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is

1. $R$
2. $(-1,1)$
3. $[-1,1]$
4. $(0,1)$

Q. The range of the function $f\left(x\right)=\frac{2+x}{2-x},x\ne 2$ is

1. $R-\{-1\}$
2. $R-\left\{1\right\}$
3. $R-\{-2\}$
4. $R$

Q.

The range of f(x) = $\frac{x^2+x+1}{x^2+x-1}$

1. (-∞ , -3/5 ] U [1, ∞)

2. (-∞ , -3/5 ) U (1, ∞)

3. None of these

4. (-∞ , -3/5 ] U (1, ∞)

Q. If ordered pair $(\alpha ,\beta )$ where $\alpha ,\beta \in I$ satisfy the equation $2x^2-3xy-2y^2=7$, then value of $\alpha +\beta$ can be

1. $5$
2. $4$
3. $-4$
4. $3$

Q.

The range of f(x) = $\frac{x^2+x+1}{x^2+x-1}$

1. $(-\infty ,\frac{-3}{5}]\bigcup [1,\infty )$

2. $(-\infty ,\frac{-3}{5}]\bigcup (1,\infty )$

3. $(-\infty ,\frac{3}{5})\bigcup (1,\infty )$

4. $(-\infty ,\frac{5}{3}]\bigcup [2,\infty )$

Q.

If $x=-2$, then find the value of each of the following algebraic expressions.

$2x-x^2$