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

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

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

inverse

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

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

Solution steps

Solve for

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

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

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

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

Solve for

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

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

Substitute

y = x

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

y = \frac{2 x ^{2}}{x ^{2} - 1}

f (x) = (\frac{- 9 - 7 x}{3})

f (x) = 8 x - 12

x^{4} - 6 x^{2} - 8

f (x) = tan (x)

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