What is the inverse of f(x)=4sin(2x+5)-7 ?

The inverse of f(x)=4sin(2x+5)-7 is (arcsin((x+7)/4)-5)/(2)

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inverse of f(x)=4sin(2x+5)-7

inverse

f (x) = 4 sin (2 x + 5) - 7

\frac{arcsin ( \frac{x + 7}{4} ) - 5}{2}

Solution steps

Solve for

sin (2 x + 5), y = 4 sin (2 x + 5) - 7

sin (2 x + 5) = \frac{y + 7}{4}

sin (a) = b \Rightarrow a = arcsin (b)

2 x + 5 = arcsin (\frac{y + 7}{4})

Solve for

x, 2 x + 5 = arcsin (\frac{y + 7}{4})

\frac{arcsin ( \frac{y + 7}{4} ) - 5}{2}

Substitute

y = x

\frac{arcsin ( \frac{x + 7}{4} ) - 5}{2}

f (x) = - \frac{1}{2} x + 7

f (x) = ln (5 x + 1) - 7

f (x) = \frac{1 - x}{1 + x}

f (x) = \frac{3 x + 1}{5}

f (x) = \frac{3 x - 1}{x + 2}

What is the inverse of f(x)=4sin(2x+5)-7 ?
The inverse of f(x)=4sin(2x+5)-7 is (arcsin((x+7)/4)-5)/(2)