Functions in Algebra Examples

Find $f(n)$ when $n=10k$, where ff satisfies the recurrence relation ${\displaystyle f\left(n\right)=f\frac{n}{10}}$ with $f(1)=10$.

prove that ${\sin }^{-1}(x)={\csc }^{-1}\left(\frac{1}{x}\right)$

Find the midpoint of the segrnent with the given encpoin's: ${\displaystyle (\frac{3}{8},-\left(\frac{2}{5}\right))}$ and ${\displaystyle (-\left(\frac{5}{2}\right),\frac{3}{2})}$

Need to find and correct error in the function $y=-9.5x^2-47.5x+63$ as shown.
$x=\frac{-b}{2a\times x}=\frac{-47.5}{2(-9.5)\times x}=\frac{-47.5}{-19\times x}=-(-2.5)x=2.5$
$y=-9.5(2.5{)}^2-47.5(2.5)+63y=59.375-118.75+63y=-115.125$

For what value of the constant c is the function f continuous on ${\displaystyle (-\infty ,+\infty )?}$
$$ ${\displaystyle f\left(x\right)=\{\left(c{x}^2\right)+4x,\left(x^3\right)-cx\}\text{if}x<5,\text{if}x\Rightarrow 5}$ c=

Sketch one cycle of each sine curve. Assume $a>0$. Write an equation for each graph. amplitude = 2 period = $\frac{\pi }{2}$

$\underset{x\to \mathrm{\infty }}{lim}{x}^{\frac{1}{lnx}}$Select one:
a 1
b 0
c ∞
d e

In right triangle RST, the two acute angles are ${\displaystyle \angle R\text{and}\angle T}$ If the ${\displaystyle \tan \left(R\right)=\frac{7}{3},whatisthe\tan \left(T\right)?}$