Trigonometry
Inverse Trigonometric Functions
MCQ (Single Correct Answer)Subjective
1
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

The even function of the following is

A
$$f(x) = {{{a^x} + {a^{ - x}}} \over {{a^x} - {a^{ - x}}}}$$
B
$$f(x) = {{{a^x} + 1} \over {{a^x} - 1}}$$
C
$$f(x) = x.\,{{{a^x} - 1} \over {{a^x} + 1}}$$
D
$$f(x) = {\log _2}(x + \sqrt {{x^2} + 1} )$$
2
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

If f(x + 2y, x $$-$$ 2y) = xy, then f(x, y) is equal to

A
$${1 \over 4}xy$$
B
$${1 \over 4}({x^2} - {y^2})$$
C
$${1 \over 8}({x^2} - {y^2})$$
D
$${1 \over 2}({x^2} + {y^2})$$
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then

A
$f(x)=\sin ^2 x, g(x)=\sqrt{x}$
B
$f(x)=\sin x, g(x)=|x|$
C
$f(x)=x^2, g(x)=\sin \sqrt{x}$
D
$f(x)=|x|, g(x)=\sin x$
4
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5

If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be

A
$x$
B
$2 x$
C
$\frac{2 x-3}{3 x-4}$
D
$\frac{3 x-4}{2 x-3}$
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