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

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

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

inverse

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}

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