What is the domain of f(x)=ln(x-1)+e^{x^2-3}+(x^2-4)^{5/3} ?

The domain of f(x)=ln(x-1)+e^{x^2-3}+(x^2-4)^{5/3} is x>1

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domain of f(x)=ln(x-1)+e^{x^2-3}+(x^2-4)^{5/3}

domain

f (x) = ln (x - 1) + e^{x^{2} - 3} + (x^{2} - 4)^{\frac{5}{3}}

x > 1

Interval Notation

(1, \infty)

Solution steps

Find positive values for logs:

x > 1

The function domain

x > 1

f (x) = x^{\frac{1}{3}}

f (x) = 3 x - 5

f (x) = (ln (x))^{2}

f (x) = \frac{1}{1 - x ^{2}}

f (x) = 6 x

What is the domain of f(x)=ln(x-1)+e^{x^2-3}+(x^2-4)^{5/3} ?
The domain of f(x)=ln(x-1)+e^{x^2-3}+(x^2-4)^{5/3} is x>1