Solve the equation $$x+3=\ \sqrt[]{x+33}.$$

The solution to the equation is 3, and −8 is an extraneous solution.

The equation has two solutions, −8 and 3.

The solution to the equation is −8 , and 3 is an extraneous solution.

The equation has no real solutions.

Let f(x) = 3x 2 + 2 and g(x) = $$\sqrt[]{x-4}$$ . What is the rule for the composition f ∘ g ?

(f ∘ g)(x) = 3x − 10, domain is x ≥ 4

(f ∘ g)(x) = $$\sqrt[]{3x^2-2}$$ , domain is all real numbers

(f ∘ g)(x) = $$\sqrt[]{3x^2-2}$$ , domain is $$x\ge4$$

(f ∘ g)(x) = 3x − 10, domain is all real numbers

Let f(x) = x 2 − 2x + 1 . Find the inverse function of f by identifying an appropriate restriction of its domain.

The inverse is $$f^{-1}\left(x\right)=\sqrt[]{x}+1$$ if the domain of f is restricted to $$x\ge1.$$

The inverse is $$f^{-1}\left(x\right)=\sqrt[]{x+1}$$ if the domain of f is restricted to $$x\ge-1.$$

The inverse is $$f^{-1}\left(x\right)=\sqrt[]{x}-1$$ if the domain of f is restricted to $$x\ge0.$$

The function does not have an inverse.

Topic 5 - Rational Exponents and Radical Functions

Authored by CJ Jung

Mathematics

9th - 12th Grade

CCSS covered

Used 8+ times

Topic 5 - Rational Exponents and Radical Functions

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MULTIPLE SELECT QUESTION

2 mins • 1 pt

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

9m³n

9m⁶n²

3m³n

3m⁸

MATH RESPONSE QUESTION

2 mins • 1 pt

Solve the equation -4x³= 32.
x = ____

Mathematical Equivalence

Tags

CCSS.8.EE.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

MATH RESPONSE QUESTION

2 mins • 1 pt

Mathematical Equivalence

Tags

CCSS.HSA.APR.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Tags

CCSS.HSN.RN.A.2

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Adding 12 to 4x translates the graph left 12 units

Adding 12 to 4x translates the graph left 3 units.

Multiplying x by 4 stretches the graph vertically by a factor of 4.

Multiplying x by 4 stretches the graph vertically by a factor of 2.

Multiplying x by 4 compresses the graph horizontally by a factor of 2.

Tags

CCSS.HSF.BF.B.3

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Topic 5 - Rational Exponents and Radical Functions

Solve the equation -4x3 = 32.x = ____

What radical function is represented by the graph?

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Solve the equation -4x³= 32.
x = ____