Precalculus Examples

$g (t) = \sqrt{8^{t} - 64}$

Step 1

Set the radicand in $\sqrt{8^{t} - 64}$ greater than or equal to $0$ to find where the expression is defined.

$8^{t} - 64 \geq 0$

Step 2

Solve for $t$ .

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Step 2.1

Add $64$ to both sides of the inequality.

$8^{t} \geq 64$

Step 2.2

Create equivalent expressions in the equation that all have equal bases.

$8^{t} \geq 8^{2}$

Step 2.3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$t \geq 2$

Step 3

The domain is all values of $t$ that make the expression defined.

Interval Notation:

$[2, \infty)$

Set-Builder Notation:

${t | t \geq 2}$

Step 4