How to Find the Inverse of a Function

Q.

Find the multiplicative inverse of ${\left(\frac{81}{16}\right)}^{(-\frac{3}{4})}$.

Q.

Find the multiplicative inverse of $3+4i$ .

Q. The inverse of the function is $f\left(x\right)=\frac{{10}^x-{10}^{-x}}{{10}^x+{10}^{-x}}+1$ is

1. $f^{-1}\left(x\right)=\frac{1}{2}lo{g}_{10}\frac{x}{2-x}$
2. $Noneofthese$
3. $f^{-1}\left(x\right)=lo{g}_{10}\frac{x}{2-x}$
4. $f^{-1}\left(x\right)=\frac{1}{2}lo{g}_{10}\frac{x}{1-x}$

Q. Let $f:R\to R,g:R\to R$, be two functions, such that f(x) =2x – 3, g (x) = $x^3$ + 5.
The function $(fog{)}^{-1}$ (x) is equal to

1. ${\left(\frac{x+7}{2}\right)}^{\frac{1}{3}}$
2. ${\left(\frac{x-2}{7}\right)}^{\frac{1}{3}}$
3. ${(x-\frac{7}{2})}^{\frac{1}{3}}$
4. ${\left(\frac{x-7}{2}\right)}^{\frac{1}{3}}$

Q.

If the sets A and B are defined as A = {(x, y) : y = $e^x$, x ∈ R};

B = {(x, y) : y = x, x ∈ R}, then

1. 

2. 

3. 

4. 

Q. The inverse of $f\left(x\right)={(5-(x-8{)}^5)}^{\frac{1}{3}}$ is

1. $5-(x-8{)}^5$
   
2. $8+(5-x^3{)}^{\frac{1}{5}}$
   
3. $8-(5-x^3{)}^{\frac{1}{5}}$
   
4. $(5-(x-8{)}^{\frac{1}{5}}{)}^3$

Q.

The least value of $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}+\mathrm{f}+\mathrm{g}+\mathrm{h}$ for possible values of $\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e},\mathrm{f},\mathrm{g},$ and $\mathrm{h}$ satisfying the condition ${\mathrm{a}}^{\frac{2}{3}}+{\mathrm{b}}^{\frac{2}{3}}+{\mathrm{c}}^{\frac{2}{3}}+{\mathrm{d}}^{\frac{2}{3}}+{\mathrm{e}}^{\frac{2}{3}}+{\mathrm{f}}^{\frac{2}{3}}+{\mathrm{g}}^{\frac{2}{3}}+{\mathrm{h}}^{\frac{2}{3}}=4$ is

1. $\sqrt{2}$

2. $2\sqrt{2}$

3. $3\sqrt{2}$

4. $4\sqrt{2}$

Q. If \(f : R \rightarrow R\) be a mapping defined by $f\left(x\right)=x^3+5$, then $f^{-1}x$ is equal to

1. $(x+5{)}^{\frac{1}{3}}$
2. $(x-5{)}^{\frac{1}{3}}$
3. $(5-x{)}^{\frac{1}{3}}$
4. $5-x$

Q. Let $f\left(x\right)=(x+1{)}^2-1,(x\ge -1)$. Then the set $S=\{x:f(x)=f^{-1}(x\left)\right\}$. is

1. $Empty$
2. $\{0,1,-1\}$
3. $\{0,-1\}$
4. $\{0,-1,\frac{-3+i\sqrt{3}}{2},\frac{-3-i\sqrt{3}}{2}\}$

Q.

If the sets A and B are defined as

A = {(x, y) : $y=\frac{1}{x}$, 0 ≠ x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then

1. 

2. 

3. None of these

4. 

Q. If the function $f:[1,\infty )\to [1,\infty )$ is defined by $f\left(x\right)=2^{x(x-1)}$, then $f^{-1}\left(x\right)$ is

1. $\frac{1}{2}(1+\sqrt{1+4lo{g}_{2}x})$
2. $\frac{1}{2}(1-\sqrt{1+4lo{g}_{2}x})$
3. ${\left(\frac{1}{2}\right)}^{x(x-1)}$
4. not defined

Q. Suppose f(x) = $(x+1{)}^2$ for $\ge$ -1. If g(x) is the function whose graph is reflection of the graph of f(x) with respect to line y = x, then g(x) equals

1. $-\sqrt{x}-1,x\ge 0$
2. $\frac{1}{(x+1{)}^2},x>-1$
3. $\sqrt{x+1},x\ge -1$
4. $\sqrt{x}-1,x\ge 0$

Q. Let $f\left(x\right)=x^2-x+1$, $x\ge \frac{1}{2}$ then the solution of the equation $f^{-1}\left(x\right)=x$ is

1. x = 1
2. x = 2
3. None of these
4. $x=\frac{1}{2}$

Q.

If the sets A and B are defined as

A = {(x, y) : y = $\frac{1}{x}$, 0 ≠ x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then

1. 

2. None of these

3. 

4. 

Q. if x+1/x=3*1/3, find the value of x³-1/x³

Q.

What is the inverse of the function { (1, 2), (2, 3), (3, 1) } from the set A ={1, 2, 3} to itself?

1. {(2, 1), (3, 3), (1, 2)}

2. {(2, 3), (1, 2), (3, 1)}

3. None of these

4. { (1, 2), (2, 3), (3, 1) }