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Popular >

f(x)=(4sin(x)-3)/(4+sin(x))

Solution

f (x) = \frac{4 sin ( x ) - 3}{4 + sin ( x )}

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{7}{3} \leq f (x) \leq \frac{1}{5}

X Intercepts : (arcsin (\frac{3}{4}) + 2 πn, 0), (π - arcsin (\frac{3}{4}) + 2 πn, 0), Y Intercepts : (0, - \frac{3}{4})

Asymptotes : None

Extreme Points : Maximum (\frac{π}{2} + 2 πn, \frac{1}{5}), Minimum (\frac{3 π}{2} + 2 πn, - \frac{7}{3})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{7}{3}, \frac{1}{5}]

Solution steps

Periodicity of

\frac{4 sin ( x ) - 3}{4 + sin ( x )} : 2 π

Domain of

\frac{4 sin ( x ) - 3}{4 + sin ( x )} : - \infty < x < \infty

Range of

\frac{4 sin ( x ) - 3}{4 + sin ( x )} : - \frac{7}{3} \leq f (x) \leq \frac{1}{5}

Axis interception points of

\frac{4 sin ( x ) - 3}{4 + sin ( x )} :

X Intercepts

: (arcsin (\frac{3}{4}) + 2 πn, 0), (π - arcsin (\frac{3}{4}) + 2 πn, 0),

Y Intercepts

: (0, - \frac{3}{4})

Asymptotes of

\frac{4 sin ( x ) - 3}{4 + sin ( x )} :

None

Extreme Points of

\frac{4 sin ( x ) - 3}{4 + sin ( x )} :

Maximum

(\frac{π}{2} + 2 πn, \frac{1}{5}),

Minimum

(\frac{3 π}{2} + 2 πn, - \frac{7}{3})

Popular Examples

y=10(t^3+4t^2+t-6)

y = 10 (t^{3} + 4 t^{2} + t - 6)

f(x)={x+2:x<0,x^2-1:0<= x<= 3,8:x>3}

f (x) = {x + 2 : x < 0, x^{2} - 1 : 0 \leq x \leq 3, 8 : x > 3}

f (x) = 3 - sin (x)

f (x) = - x^{3} - 4 x^{2}

f(x)=4x^3+3x^2+6x+5

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

Frequently Asked Questions (FAQ)

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