Given $f=x^3$ and $g(x)=2x+5$ find

a$.(f$@$g)(x)$

b$.(g$@$f)(x)$

State the smallest and largest values in the interval, $[5,9).$

Find the slope of the line segment that intersects the graph of the function $f(x)=x^2$ at

a$.,x=2$ and $x=4.$

b$.,x=2$ and $x=2\mathrm{.}5.$

c$.,x=2$ and $x=2\mathrm{.}1.$

Given $f(x)=2^x,$ find the ratio:

a$.\frac{f(8)}{f(5)}$

b$.\frac{f(7\mathrm{.}2)}{f(4\mathrm{.}2)}$

Solve for $x$ :

$7^x=87$

Prove the following identity: $si{n}^2+co{s}^2=1.$