Rational function

Q. If $f\left(x\right)=x+\frac{1}{x},x\ne 0;\mathrm{then}{\left(f\left(x\right)\right]}^3=$

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

Q. If f(x) = $x^2$ + 1 and g(x) = x - 1, then fog(3) =.

1. 6
2. 5
3. 7

Q.

Let $f\left(x\right)=x^2$ and $g\left(x\right)=3x+4$. Find the value of $\frac{(f+g)\left(x\right)}{(f-g)\left(x\right)}$ when $x=1$

1. $\frac{-4}{3}$

2. $\frac{-3}{4}$

3. $\frac{4}{3}$

4. $\frac{3}{4}$

Q.

If f(x) = $\sqrt{x}$ and $g\left(x\right)=x$ , then $\left(\frac{f}{g}\right)\left(x\right)$ equals to $(x\ne 0)$

1. $\sqrt{x}$

2. $x^{\frac{3}{2}}$

3. $x$

4. $\frac{1}{\sqrt{x}}$

Q. If $f\left(x\right)=\frac{4^x}{4^x+2}\mathrm{for}\mathrm{all}x\in R.$
Which of the following is/are true?

1. $f\left(x\right)=f(1-x)$
2. $f\left(x\right)+f(1-x)=0$
3. $f\left(x\right)+f(1-x)=1$
4. $f\left(x\right)+f(x-1)=1$