Alg2 Unit 5 Test - Radicals Equations

If f(x) = x – 5 and g(x) = 𝑥 ² + 3, find f [g(–2)].

(a)  

What is the inverse function of ( f(x) = 5x + 10 )?

Be sure to write fractions using the fraction key

Explain why ( f(x) = 5x - 3 ) and $$g\ \left(x\right)=\left(\frac{\left(x+3\right)}{5}\right)$$ are inverse functions (or not).

In other words, if they are inverses, how so? If they are not inverses, how do you know?

What is the domain of $$y\ =\ \sqrt[]{2x-8}$$

What is the range of $$y\ =\ \sqrt[]{2x-8}$$

Combine and Simplify

$$5\sqrt[]{72}+\sqrt[]{75}-\sqrt[]{288}$$

Simplify

$$\sqrt[3]{24a^6b^5}$$

Simplify

$$\sqrt[]{98x^6y^4}$$

Simplify

$$\sqrt[]{\frac{25}{169}}$$

Write the radical $$\sqrt[5]{32x^3}$$ using rational exponents

be sure to simplify the coefficient

The diameter of a tree d (in inches) is related to its basal area BA (in square feet) by the formula $$d\ =\sqrt[]{\frac{576\left(BA\right)}{\pi}}$$ . If the basal area (BA) of a tree is 12.4 square feet, what is the diameter of the tree? Use a calculator to approximate your answer to three decimal places. Use 3.14 for π.

Simplify this expression (keep your answer as a rational exponent)

$$\frac{x}{x^{\frac{1}{2}}\times x^{\frac{1}{3}}}$$

Solve

$$\sqrt[3]{3x+1}=4$$

(a)  

What is √34 divided by √51 in simplest radical form?

(a)  

(a)  

Solve for k.

(a)