What is the domain of f(x)=log_{x+3}(-2x+3) ?

The domain of f(x)=log_{x+3}(-2x+3) is -3<x<-2\lor-2<x< 3/2

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domain of f(x)=log_{x+3}(-2x+3)

domain

f (x) = lo g_{x + 3} (- 2 x + 3)

- 3 < x < - 2 or - 2 < x < \frac{3}{2}

Interval Notation

(- 3, - 2) \cup (- 2, \frac{3}{2})

Solution steps

Check logs domain:

- 3 < x < - 2 or - 2 < x < \frac{3}{2}

The function domain

- 3 < x < - 2 or - 2 < x < \frac{3}{2}

f (x) = x^{2} + x - 5

f (x) = lo g_{10} (x^{2} + 9 x + 8)

\frac{2 x}{x - 4}

\frac{x}{- x + 4}

f (x) = - 3^{2}

What is the domain of f(x)=log_{x+3}(-2x+3) ?
The domain of f(x)=log_{x+3}(-2x+3) is -3<x<-2\lor-2<x< 3/2