What is the f(x)=(3x)/(sqrt(16-x^2))-(4x)/(5-|3x-2|) ?

The f(x)=(3x)/(sqrt(16-x^2))-(4x)/(5-|3x-2|) is

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f(x)=(3x)/(sqrt(16-x^2))-(4x)/(5-|3x-2|)

f (x) = \frac{3 x}{16 - x ^{2}} - \frac{4 x}{5 - ∣ 3 x - 2 ∣}

Domain : - 4 < x < - 1 or - 1 < x < \frac{7}{3} or \frac{7}{3} < x < 4

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

Y Intercepts : (0, 0)

Asymptotes : Vertical x = - 4, x = - 1, x = \frac{7}{3}, x = 4

Extreme Points : Maximum (- 2.05856 \dots, - 4.39359 \dots), Minimum (0.32665 \dots, - 0.08248 \dots), Maximum (\frac{2}{3}, \frac{3}{35} - \frac{8}{15}), Minimum (3.24440 \dots, 8.90827 \dots)

Interval Notation

Domain : (- 4, - 1) \cup (- 1, \frac{7}{3}) \cup (\frac{7}{3}, 4)

Range : (- \infty, \infty)

Solution steps

Domain of

\frac{3 x}{16 - x ^{2}} - \frac{4 x}{5 - ∣ 3 x - 2 ∣} : - 4 < x < - 1 or - 1 < x < \frac{7}{3} or \frac{7}{3} < x < 4

Range of

\frac{3 x}{16 - x ^{2}} - \frac{4 x}{5 - ∣ 3 x - 2 ∣} : - \infty < f (x) < \infty

Axis interception points of

\frac{3 x}{16 - x ^{2}} - \frac{4 x}{5 - ∣ 3 x - 2 ∣} :

Y Intercepts

: (0, 0)

Asymptotes of

\frac{3 x}{16 - x ^{2}} - \frac{4 x}{5 - ∣ 3 x - 2 ∣} :

Vertical

: x = - 4, x = - 1, x = \frac{7}{3}, x = 4

Extreme Points of

\frac{3 x}{16 - x ^{2}} - \frac{4 x}{5 - ∣ 3 x - 2 ∣} :

Maximum

(- 2.05856 \dots, - 4.39359 \dots),

Minimum

(0.32665 \dots, - 0.08248 \dots),

Maximum

(\frac{2}{3}, \frac{3}{35} - \frac{8}{15}),

Minimum

(3.24440 \dots, 8.90827 \dots)

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

f (x) = - 4 (x + 2) (x - 3)

f (x) = - x^{2} + 12 x + 80

What is the f(x)=(3x)/(sqrt(16-x^2))-(4x)/(5-|3x-2|) ?
The f(x)=(3x)/(sqrt(16-x^2))-(4x)/(5-|3x-2|) is