What is the domain of f(x)=sqrt(5x-30)+ln(21-3x) ?

The domain of f(x)=sqrt(5x-30)+ln(21-3x) is 6<= x<7

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domain of f(x)=sqrt(5x-30)+ln(21-3x)

domain

f (x) = 5 x - 30 + ln (21 - 3 x)

6 \leq x < 7

Interval Notation

[6, 7)

Solution steps

Find non-negative values for radicals:

x \geq 6

Find positive values for logs:

x < 7

Combine real regions and undefined points for final function domain

6 \leq x < 7

y = - (1 - x)^{2} + 3

∣ x ∣ + x

∣ x ∣ - 5

f (x) = \frac{3 x + 4}{x ^{2} - 5 x + 6}

- \frac{19}{( 3 + x ) ^{2}}

What is the domain of f(x)=sqrt(5x-30)+ln(21-3x) ?
The domain of f(x)=sqrt(5x-30)+ln(21-3x) is 6<= x<7