If $y = f(x) = \frac{{ax + b}}{{cx - a}}$, then $x$ is equal to
$1/f(x)$
$1/f(y)$
$yf(x)$
$f(y)$
(d) $y = \frac{{ax + b}}{{cx – a}}$
$⇒ x(cy – a) = b + ay$
$⇒ x = \frac{{ay + b}}{{cy – a}} = f(y)$.
If $h\left( x \right) = \left[ {\ln \frac{x}{e}} \right] + \left[ {\ln \frac{e}{x}} \right]$ ,where [.] denotes greatest integer function, then which of the following is false ?
If $\,\,f(x) = \left\{ {\begin{array}{*{20}{c}} {3 + x;\,\,\,\,\,x \geqslant 0} \\ {2 – 3x;\,\,\,\,\,x < 0} \end{array}} \right.$ then $\mathop {\lim }\limits_{x \to 0} f(f(x))$ is equal to –
If $f(x) = \frac{{{x^2} – 1}}{{{x^2} + 1}}$, for every real numbers. then the minimum value of $f$
If for the function $f(x) = \frac{1}{4}{x^2} + bx + 10$ ; $f\left( {12 – x} \right) = f\left( x \right)\,\forall \,x\, \in \,R$ , then the value of $'b'$ is
The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$
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