Match List-I with List-II
| Match-I | Match-II | ||
| (A) | $x=2at^2,y=at^4$ | (I) | Inverse trignometric function |
| (C) | $f(x)=(2x=3)^3$ | (II) | Implicit function |
| (C) | $xy +y^2=tan(x+y)$ | (III) | Parametric function |
| (D) | $y=tan^{-1}\left(\frac{3x-x^3}{1-3x^2}\right), -\frac{1}{\sqrt{3}}< x < \frac{1}{\sqrt{3}}$ | (IV) | Composite function |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 1
Match each expression with its type.
(A) $x=2at^{2},\; y=at^{4}$
Both $x$ and $y$ are expressed in terms of a parameter $t$.
So it is a parametric function.
(A) → (III).
(B) $f(x)=(2x-3)^{3}$
This is a composition of functions: $2x-3$ and $(\cdot)^3$.
So it is a composite function.
(B) → (IV).
(C) $xy+y^{2}=\tan(x+y)$
$y$ is not explicitly expressed in terms of $x$.
So it is an implicit function.
(C) → (II).
(D) $y=\tan^{-1}\!\left(\frac{3x-x^{3}}{1-3x^{2}}\right)$
This involves an inverse trigonometric function.
(D) → (I).
final answer: (A)–(III), (B)–(IV), (C)–(II), (D)–(I)