40
MCQ (Single Correct Answer)
If $f: R \rightarrow R$ be the functions defined by $f(x)=x^3+5$, then $f^{-1}(x)$ is
A
$(x+5)^{\frac{1}{3}}$
B
$(x-5)^{\frac{1}{3}}$
C
$(5-x)^{\frac{1}{3}}$
D
$5-x$
41
MCQ (Single Correct Answer)
If $f: A \rightarrow B$ and $g: B \rightarrow C$ be the bijective functions, then $(g \circ f)^{-1}$ is
A
$f^{-1} \mathrm{og}^{-1}$
B
$f \circ g$
C
$g^{-1} o f^{-1}$
D
$g \circ f$
42
MCQ (Single Correct Answer)
If $f: R-\left\{\frac{3}{5}\right\} \rightarrow R$ be defined by $f(x)=\frac{3 x+2}{5 x-3}$, then
A
$f^{-1}(x)=f(x)$
B
$f^{-1}(x)=-f(x)$
C
$(f \circ f) x=-x$
D
$f^{-1}(x)=\frac{1}{19} f(x)$
43
MCQ (Single Correct Answer)
If $f:[0,1] \rightarrow[0,1]$ be defined by $f(x)=\left\{\begin{array}{cc}x, & \text { if } x \text { is rational } \\ 1-x, & \text { if } x \text { is irrational }\end{array}\right.$ then $(f \circ f) x$ is
A
constant
B
$1+x$
C
$x$
D
None of these
44
MCQ (Single Correct Answer)
If $f:[2, \infty) \rightarrow R$ be the function defined by $f(x)=x^2-4 x+5$, then the range of $f$ is
A
$R$
B
$[1, \infty)$
C
$[4, \infty)$
D
$[5, \infty)$