5.7 Inverses and radical functions  (Page 6/7)

$f\left(x\right)=\sqrt{6x-8}+5$

$f\left(x\right)=9+2\sqrt[3]{x}$

$f\left(x\right)=3-\sqrt[3]{x}$

$f\left(x\right)=\frac{2}{x+8}$

$f\left(x\right)=\frac{3}{x-4}$

$f\left(x\right)=\frac{x+3}{x+7}$

$f\left(x\right)=\frac{x-2}{x+7}$

$f\left(x\right)=\frac{3x+4}{5-4x}$

$f\left(x\right)=\frac{5x+1}{2-5x}$

$f(x)=x^2+2x, [\mathrm{-1},\infty )$

$f(x)=x^2+4x+1, [\mathrm{-2},\infty )$

$f(x)=x^2-6x+3, [3,\infty )$

$f(x)=x^2+2,x\ge 0$

$f(x)=4-x^2,x\ge 0$

$f(x)={\left(x+3\right)}^2,x\ge -3$

$f(x)={\left(x-4\right)}^2,x\ge 4$

$f(x)=x^3+3$

$f(x)=1-x^3$

$f(x)=x^2+4x,x\ge -2$

$f(x)=x^2-6x+1,x\ge 3$

$f(x)=\frac{2}{x}$

$f(x)=\frac{1}{x^2},x\ge 0$

$f(x)=\sqrt{\frac{(x+1)(x-1)}{x}}$

$f(x)=\sqrt{\frac{(x+2)(x-3)}{x-1}}$

$f(x)=\sqrt{\frac{x(x+3)}{x-4}}$

$f(x)=\sqrt{\frac{x^2-x-20}{x-2}}$

$f(x)=\sqrt{\frac{9-x^2}{x+4}}$

$f(x)=x^3-x-2,y=1,2,3$

$f(x)=x^3+x-2,y=0,1,2$

$f(x)=x^3+3x-4,y=0,1,2$

$f(x)=x^3+8x-4,y=-1,0,1$

$f(x)=x^4+5x+1,y=-1,0,1$

$f(x)=a{x}^3+b$

$f(x)=x^2+bx$

$f(x)=\sqrt{a{x}^2+b}$

$f(x)=\sqrt[3]{ax+b}$

$f(x)=\frac{ax+b}{x+c}$

An object dropped from a height of 200 meters has a height, $h\left(t\right),$ in meters after $t$ seconds have lapsed, such that $h(t)=200-4.9t^2.$ Express $t$ as a function of height, $h,$ and find the time to reach a height of 50 meters.

An object dropped from a height of 600 feet has a height, $h\left(t\right),$ in feet after $t$ seconds have elapsed, such that $h(t)=600-16t^2.$ Express $t$ as a function of height $h,$ and find the time to reach a height of 400 feet.

The volume, $V,$ of a sphere in terms of its radius, $r,$ is given by $V(r)=\frac{4}{3}\pi r^3.$ Express $r$ as a function of $V,$ and find the radius of a sphere with volume of 200 cubic feet.

The surface area, $A,$ of a sphere in terms of its radius, $r,$ is given by $A(r)=4\pi r^2.$ Express $r$ as a function of $V,$ and find the radius of a sphere with a surface area of 1000 square inches.

A container holds 100 mL of a solution that is 25 mL acid. If $n$ mL of a solution that is 60% acid is added, the function $C(n)=\frac{25+.6n}{100+n}$ gives the concentration, $C,$ as a function of the number of mL added, $n.$ Express $n$ as a function of $C$ and determine the number of mL that need to be added to have a solution that is 50% acid.

The period $T,$ in seconds, of a simple pendulum as a function of its length $l,$ in feet, is given by $T(l)=2\pi \sqrt{\frac{l}{32.2}}$ . Express $l$ as a function of $T$ and determine the length of a pendulum with period of 2 seconds.

The volume of a cylinder , $V,$ in terms of radius, $r,$ and height, $h,$ is given by $V=\pi r^{2}h.$ If a cylinder has a height of 6 meters, express the radius as a function of $V$ and find the radius of a cylinder with volume of 300 cubic meters.

The surface area, $A,$ of a cylinder in terms of its radius, $r,$ and height, $h,$ is given by $A=2\pi r^2+2\pi rh.$ If the height of the cylinder is 4 feet, express the radius as a function of $V$ and find the radius if the surface area is 200 square feet.

The volume of a right circular cone, $V,$ in terms of its radius, $r,$ and its height, $h,$ is given by $V=\frac{1}{3}\pi r^{2}h.$ Express $r$ in terms of $h$ if the height of the cone is 12 feet and find the radius of a cone with volume of 50 cubic inches.

Consider a cone with height of 30 feet. Express the radius, $r,$ in terms of the volume, $V,$ and find the radius of a cone with volume of 1000 cubic feet.