Question5 Q.13) If $f(x)=\frac{\sec x}{x+3}$ and $f^{-1}(c)=0$, then $c=$ A. $\frac{1}{3}$ B. 0 C. $\frac{2}{\sqrt{3}}$ D. $\frac{1}{4}$ cibtifantstius orsil $2=$ Q.14) One of the following equations is symmetric about origin A. $y=\frac{x+1}{x}$ B. $-x^{5}+3 x$ C. $y=x^{4}-2 x^{2}+6$ D. None $$\begin{aligned} -2= & \left.-x^{5}\right)^{3 x} \\ & -\left(x^{5}\right. \end{aligned}$$ Q.15) One of the following functions is an even function A. $f(x)=\frac{\sec 4 x}{5 x}$ B.None C. $f(x)=\frac{\cos 5 x}{2 x}$ D. $f(x)=\frac{\sin 2 x}{3 x}$ Q.16)The range of the function $f(x)=\frac{1}{\sqrt{4-x^{2}}}$ is A. $(0,2)$ B. $[0,2]$ C. $\left(\frac{1}{2}, \infty\right)$ D. $\left[\frac{1}{2}, \infty\right)$ E.None Q.17) Given that $f(x)=\frac{1}{x-3}$ and $g(x)=\frac{1}{x}$ then the domain of the function $f \circ g$ is A. $R \backslash\left\{0, \frac{1}{3}\right\}$ $B . R \backslash\{0\}$ C. $R \backslash\left\{\frac{1}{3}\right\}$ D. $R \backslash\{0,3\}$ E.None Q.18) (The greatest integer less than or equals $x$ ) The range of $f(x)=2[x]$ is A. $\{0,61,62,63$, $\qquad$ B. $R \backslash\{0,61,62,63$ $\qquad$ $f|x|$ sec - C. $\{0,62,64,66$ $\qquad$ D. $(-\infty, \infty)$ Q.19) If the domain of the function $y=f(x)$ is $[2,3)$ then the domain of $g(x)=f(3-x)$ is A. $[2,3)$ B. $(0,1]$ C. $[0,1)$ D. $(2,3]$ E.None Q.20) Given that $f(x)=\sec ^{-1} x$ then $f(2)=$ A. $\frac{1}{\sin 2}$ B. $\frac{1}{\cos 2}^{x}$ C. $\cos ^{-1}\left(\frac{1}{2}\right)$ D. $\sin ^{-1}\left(\frac{1}{2}\right)$ E.None Q.21) Given that $f(x)=x^{2}$ and $g(x)=\left\{\begin{array}{l}2 x, \\ x+3, x \geq 4\end{array}\right.$ then $\left.(f \circ g)(x)=f(x)\right)$ A. $\left\{\begin{array}{cl}4 x^{2} & , x<4 \\ (x+1)^{2} & , x \geq 4\end{array}\right.$ B. $\left\{\begin{array}{cl}4 x^{2} & , x \leq 4 \\ (x+1)^{2} & , x>4\end{array}\right.$ C. $\left\{\begin{array}{cc}4 x^{2} & , \quad x<16 \\ (x+1)^{2} & , \quad x \geq 16\end{array}\right.$ D. $\left\{\begin{array}{cc}4 x^{2} & , x \leq 16 \\ (x+1)^{2} & , x>16\end{array}\right.$ Q.22) The domain of the function $f(x)=\operatorname{Ln}(5-|7 x+3|)$ is A. $\left[-\frac{8}{7}, \frac{2}{7}\right]$ B. $\left(-\frac{8}{7}, \frac{2}{7}\right)$ C. $R \backslash\left[-\frac{8}{7}, \frac{2}{7}\right]$ D. $\mathrm{R} \backslash\left(-\frac{8}{7}, \frac{2}{7}\right)$ Q.23) The domain of $f(x)=\cos ^{-1}(3 x+1)$ is $$-1,1$$ $-24-$ ولا تعت: