Linear Functions

Q. If $f(2x+3y,2x-7y)=20x$, then $f(x,y)$ equals

1. 7x-3y
2. 7x+3y
3. 3x-7y
4. x-4y

Q. Find the graph of the function $f\left(x\right)=a^x$ where $0<a<1.$

1. 

2. 

3. 

4. 

Q. Which of the following functions are identical?

1. $f\left(x\right)=\ln x^2\mathrm{and}g\left(x\right)=2\ln x$
2. $f\left(x\right)={\log }_{x}e\mathrm{and}g\left(x\right)=\frac{1}{{\log }_{e}x}$
3. $f\left(x\right)=\sin \left({\cos }^{-1}x\right)\mathrm{and}g\left(x\right)=\cos \left({\sin }^{-1}x\right)$
4. None of these

Q. Let $N$ be the set of natural numbers. Suppose $f:N\to N$ is a function satisfying the following conditions
$\left(a\right)f(m+n)=f\left(m\right)+f\left(n\right)\left(b\right)f\left(2\right)=2$
The value of $\frac{1}{7}\sum _{k=1}^{20}f\left(k\right)$ is

Q. If for non-zero x, $2f\left(x\right)+3f\left(\frac{1}{x}\right)=\frac{1}{x}-5$, then the value of f(2) is