Questions in mathematics

Questions in mathematics

[Free] Which expression is equivalent to the following complex fraction? [tex]$\frac{\frac{3}{x-1}-4}{2-\frac{2}{x-1}}$[/tex]

[Free] The function $f(x)=x^3+3$ is one-to-one. a. Find an equation for $f^{-1}$, the inverse function. b. Verify that your equation is correct by showing that $f(f^{-1}(x))=x$ and $f^{-1}(f(x))=x$. a. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression.) A. $f^{-1}(x)=\sqrt[3]{x-3}$, for all $x$ B. $f^{-1}(x)=$, for $x \geq$ $\square$ C. $f^{-1}(x)=$, for $x \leq$ $\square$ D. $f^{-1}(x)=$, for $x \neq$\square b. Verify that the equation is correct. $\begin{aligned} f(f^{-1}(x)) & =f(\square) & \text { and } & f^{-1}(f(x)) \end{aligned}=f^{-1}(\square)=\square$\n$\square$ Substitute. Simplify.

[Free] Select the correct answer. Function [tex]$h$[/tex] is the product of functions [tex]$f$[/tex] and [tex]$g$[/tex]. [tex] \begin{array}{l} f(x)=2 x+5 \ g(x)=6 x-9 \end{array} [/tex] Which equation defines function [tex]$h$[/tex]? A. [tex]$h(x)=12 x^2-4 x-45$[/tex] B. [tex]$h(x)=12 x^2-45$[/tex] C. [tex]$h(x)=12 x-45$[/tex] D. [tex]$h(x)=12 x^2+12 x-45$[/tex]

[Free] Find an explicit formula for the geometric sequence $120, 60, 30, 15, \ldots$. Note: the first term should be $a(1)$. $a(n) =$

[Free] In a study of 1350 elementary school children, 118 out of the 615 girls in the study said they want to be a teacher when they grow up. What percent of the study's participants were boys? Round to one decimal place. A. 19.2% B. 54.4% C. 45.6% D. 83.7%

[Free] Evaluate [tex]\lim _{x \rightarrow 0} \frac{e^x-e^{-x}}{\sin x}=\square[/tex]

[Free] When the function is given in vertex form $y=a(x-h)^2+k$, how is the vertex found? A. $(k, h)$ B. $(x, y)$ C. $(h, k)$ D. $(y, x)$

[Free] Select the correct arithmetic symbols that satisfy the equation: 28 _ 66 _ 25 _ 55 _ 14 = 21 Options: (1) + × ÷ - (2) × - ÷ + (3) - × ÷ + (4) + - × ÷

[Free] Divide: 48 × (√2 / 1) × 25√3 × 49√5 by 7√3 × 5√2.

[Free] Two friends, Farhan and Zoya, started from point F towards point Q at 10:00 am. Each of them, after reaching Q, immediately returned back to point P. If Farhan took 6 hours and Zoya took 12 hours for the journey, then at what time did they cross each other?