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Popular >

f(x)=ln((2x-5)(3x^2-5))

Solution

f (x) = ln ((2 x - 5) (3 x^{2} - 5))

Solution

Domain : - \frac{5}{3} < x < \frac{5}{3} or x > \frac{5}{2}

Range : - \infty < f (x) < \infty

X Intercepts : (2.53501 \dots, 0), (1.23875 \dots, 0), (- 1.27377 \dots, 0), Y Intercepts : (0, 2 ln (5))

Asymptotes : Vertical x = - \frac{5}{3}, x = \frac{5}{3}, x = \frac{5}{2}

Extreme Points : Maximum (\frac{5 - 3 5}{6}, ln (\frac{135 5 - 275}{18} + 25))

+1

Interval Notation

Domain : (- \frac{5}{3}, \frac{5}{3}) \cup (\frac{5}{2}, \infty)

Range : (- \infty, \infty)

Solution steps

Domain of

ln ((2 x - 5) (3 x^{2} - 5)) : - \frac{5}{3} < x < \frac{5}{3} or x > \frac{5}{2}

Range of

ln ((2 x - 5) (3 x^{2} - 5)) : - \infty < f (x) < \infty

Axis interception points of

ln ((2 x - 5) (3 x^{2} - 5)) :

X Intercepts

: (2.53501 \dots, 0), (1.23875 \dots, 0), (- 1.27377 \dots, 0),

Y Intercepts

: (0, 2 ln (5))

Asymptotes of

ln ((2 x - 5) (3 x^{2} - 5)) :

Vertical

: x = - \frac{5}{3}, x = \frac{5}{3}, x = \frac{5}{2}

Extreme Points of

ln ((2 x - 5) (3 x^{2} - 5)) :

Maximum

(\frac{5 - 3 5}{6}, ln (\frac{135 5 - 275}{18} + 25))

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Frequently Asked Questions (FAQ)

What is the f(x)=ln((2x-5)(3x^2-5)) ?
The f(x)=ln((2x-5)(3x^2-5)) is