8.7 Use Radicals in Functions

Before you get started, take this readiness quiz.

Solve: $1 - 2 x \geq 0 .$
If you missed this problem, review the reference.

For $f \left(x\right) = 3 x - 4 ,$ evaluate $f \left(2\right) , f \left(−1\right) , f \left(0\right) .$
If you missed this problem, review the reference.

Graph $f \left(x\right) = \sqrt{x} .$ State the domain and range of the function in interval notation.
If you missed this problem, review the reference.

For the function $f \left(x\right) = \sqrt{2 x - 1} ,$ find ⓐ $f \left(5\right)$ ⓑ $f \left(−2\right) .$

For the function $f \left(x\right) = \sqrt{3 x - 2} ,$ find ⓐ $f \left(6\right)$ ⓑ $f \left(0\right) .$

For the function $g \left(x\right) = \sqrt{5 x + 5} ,$ find ⓐ $g \left(4\right)$ ⓑ $g \left(−3\right) .$

For the function $g \left(x\right) = \sqrt[3]{x - 6} ,$ find ⓐ $g \left(14\right)$ ⓑ $g \left(−2\right) .$

For the function $g \left(x\right) = \sqrt[3]{3 x - 4} ,$ find ⓐ $g \left(4\right)$ ⓑ $g \left(1\right) .$

For the function $h \left(x\right) = \sqrt[3]{5 x - 2} ,$ find ⓐ $h \left(2\right)$ ⓑ $h \left(−5\right) .$

For the function $f \left(x\right) = \sqrt[4]{5 x - 4} ,$ find ⓐ $f \left(4\right)$ ⓑ $f \left(−12\right)$

For the function $f \left(x\right) = \sqrt[4]{3 x + 4} ,$ find ⓐ $f \left(4\right)$ ⓑ $f \left(−1\right) .$

For the function $g \left(x\right) = \sqrt[4]{5 x + 1} ,$ find ⓐ $g \left(16\right)$ ⓑ $g \left(3\right) .$

Find the domain of the function, $f \left(x\right) = \sqrt{3 x - 4} .$ Write the domain in interval notation.

Find the domain of the function, $f \left(x\right) = \sqrt{6 x - 5} .$ Write the domain in interval notation.

Find the domain of the function, $f \left(x\right) = \sqrt{4 - 5 x} .$ Write the domain in interval notation.

Find the domain of the function, $g \left(x\right) = \sqrt{\frac{6}{x - 1}} .$ Write the domain in interval notation.

Find the domain of the function, $f \left(x\right) = \sqrt{\frac{4}{x + 3}} .$ Write the domain in interval notation.

Find the domain of the function, $h \left(x\right) = \sqrt{\frac{9}{x - 5}} .$ Write the domain in interval notation.

Find the domain of the function, $f \left(x\right) = \sqrt[3]{2 x^{2} + 3} .$ Write the domain in interval notation.

Find the domain of the function, $f \left(x\right) = \sqrt[3]{3 x^{2} - 1} .$ Write the domain in interval notation.

Find the domain of the function, $g \left(x\right) = \sqrt[3]{5 x - 4} .$ Write the domain in interval notation.

Evaluate each function.

$f \left(x\right) = \sqrt{4 x - 4} ,$ find ⓐ $f \left(5\right)$ ⓑ $f \left(0\right) .$

Evaluate each function.

$g \left(x\right) = \sqrt{6 x + 1} ,$ find ⓐ $g \left(4\right)$ ⓑ $g \left(8\right) .$

Evaluate each function.

$F \left(x\right) = \sqrt{3 - 2 x} ,$ find ⓐ $F \left(1\right)$ ⓑ $F \left(−11\right) .$

Evaluate each function.

$G \left(x\right) = \sqrt{5 x - 1} ,$ find ⓐ $G \left(5\right)$ ⓑ $G \left(2\right) .$

Evaluate each function.

$g \left(x\right) = \sqrt[3]{2 x - 4} ,$ find ⓐ $g \left(6\right)$ ⓑ $g \left(−2\right) .$

Evaluate each function.

$h \left(x\right) = \sqrt[3]{x^{2} - 4} ,$ find ⓐ $h \left(−2\right)$ ⓑ $h \left(6\right) .$

Evaluate each function.

For the function $f \left(x\right) = \sqrt[4]{2 x^{3}} ,$ find ⓐ $f \left(0\right)$ ⓑ $f \left(2\right) .$

Evaluate each function.

For the function $g \left(x\right) = \sqrt[4]{4 - 4 x} ,$ find ⓐ $g \left(1\right)$ ⓑ $g \left(−3\right) .$

Find the domain of the function and write the domain in interval notation.

$f \left(x\right) = \sqrt{3 x - 1}$

Find the domain of the function and write the domain in interval notation.

$g \left(x\right) = \sqrt{2 - 3 x}$

Find the domain of the function and write the domain in interval notation.

$h \left(x\right) = \sqrt{\frac{5}{x - 2}}$

Find the domain of the function and write the domain in interval notation.

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

Find the domain of the function and write the domain in interval notation.

$g \left(x\right) = \sqrt[3]{8 x - 1}$

Find the domain of the function and write the domain in interval notation.

$f \left(x\right) = \sqrt[3]{4 x^{2} - 16}$

Find the domain of the function and write the domain in interval notation.

$F \left(x\right) = \sqrt[4]{8 x + 3}$

Find the domain of the function and write the domain in interval notation.

$G \left(x\right) = \sqrt[5]{2 x - 1}$

Explain how to find the domain of a fourth root function.

Explain why $y = \sqrt[3]{x}$ is a function.