What is the inverse of f(x)=e^{arcsin(5x+7)} ?

The inverse of f(x)=e^{arcsin(5x+7)} is (sin(ln(x))-7)/5

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inverse of f(x)=e^{arcsin(5x+7)}

inverse

f (x) = e^{a r c s i n (5 x + 7)}

\frac{sin ( ln ( x ) ) - 7}{5}

Solution steps

Solve for

arcsin (5 x + 7), y = e^{a r c s i n (5 x + 7)}

arcsin (5 x + 7) = ln (y)

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

5 x + 7 = sin (ln (y))

Solve for

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

\frac{sin ( ln ( y ) ) - 7}{5}

Substitute

y = x

\frac{sin ( ln ( x ) ) - 7}{5}

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

\frac{2}{x - 7}

e^{\frac{3}{z ^{2}}}

f (x) = \frac{5}{3} x - \frac{5}{3}

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

What is the inverse of f(x)=e^{arcsin(5x+7)} ?
The inverse of f(x)=e^{arcsin(5x+7)} is (sin(ln(x))-7)/5