Quiz I : Concept of Function

Answer all questions. Each question carries 25 marks.

Q1. Which of the following do/does not satisfy the statement "y is not a function of x" :

(i) $y=6x^3+9x^2-4x+3$

(ii) $y^2=6x+7$

(iii) $\sin y=\cos x+\tan x$

Q2. What is the domain and range of the following function:

(i) $f\left(x\right)=3x+4$

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

(iii) $f\left(x\right)=\sqrt{2x^2-4}$

Q3. Evaluate the following function at the given argument value:

(i) $f\left(x\right)=3x+4$ when $x=5$

(ii) $f\left(x\right)=\frac{1}{3x-4}+\frac{5}{2x+4}$ when $x=10$

(iii) $f\left(x\right)={(3x+5)}^4$ when $x=-2$

Q4. If $f\left(x\right)=3x^2+4\sin x-5$, simplify the following function:

(i) $f(x+4)$

(ii) $f\left(\frac{1}{x}\right)$

(ii) $f\left(\sqrt{x}\right)$