38
MCQ (Single Correct Answer)
If $f: R \rightarrow R$ be defined by $f(x)=3 x^2-5$ and $g: R \rightarrow R$ by $g(x)=\frac{x}{x^2+1}$. Then, $g \circ f$ is
A
$\frac{3 x^2-5}{9 x^4-30 x^2+26}$
B
$\frac{3 x^2-5}{9 x^4-6 x^2+26}$
C
$\frac{3 x^2}{x^4+2 x^2-4}$
D
$\frac{3 x^2}{9 x^4+30 x^2-2}$
39
MCQ (Single Correct Answer)
Which of the following functions from $Z$ into $Z$ are bijections?
A
$f(x)=x^3$
B
$f(x)=x+2$
C
$f(x)=2 x+1$
D
$f(x)=x^2+1$
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
$f^{-1}(x)=\frac{1}{19} f(x)$