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. 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

Q. If the domain of function f is set A and domain of function g is set B, then the domain of function f + g is

1. $A\cup B$
2. $A\cap B$
3. A+B
4. A-B

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. The function $f\left(x\right)=\frac{9x}{5}+32$ is the formula to convert $x^{\circ }C$ to Fahrenheit units. Then at what ${}^{\circ }C$ both Celsius and Fahrenheit is same?

1. ${32}^{\circ }C$
2. $-{32}^{\circ }C$
3. ${40}^{\circ }C$
4. $-{40}^{\circ }C$

Q. If $f:Z\to Z$ be a linear function such that $f\left(2\right)+f\left(1\right)=4,f\left(2\right)-2f\left(1\right)=-1$, then $f\left(3\right)$ is

1. $1$
2. $3$
3. $2$
4. $\frac{2}{3}$

Q. Which of the following graphs represent a linear function (over its whole domain)?

1. Only $\left(1\right)$ and $\left(2\right)$
2. Only $\left(1\right),\left(2\right)$ and $\left(3\right)$
3. $\left(1\right),\left(2\right),\left(3\right)$ and $\left(4\right)$
4. Only $\left(2\right)$

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 there are exactly two distinct linear functions which map's from $[-1,1]\text{to}[0,2].$ Then those functions are

1. $x+1$
2. $-x+1$
3. $x-1$
4. $-1-x$

Q. A function f is defined by f ( x ) = 2 x – 5. Write down the values of (i) f (0), (ii) f (7), (iii) f (–3)