What is the inverse of f(x)=((x^{1/3}+5)/(10))^7 ?

The inverse of f(x)=((x^{1/3}+5)/(10))^7 is 1000x^{3/7}-1500x^{2/7}+750\sqrt[7]{x}-125

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inverse of f(x)=((x^{1/3}+5)/(10))^7

inverse

f (x) = (\frac{x ^{\frac{1}{3}} + 5}{10})^{7}

1000 x^{\frac{3}{7}} - 1500 x^{\frac{2}{7}} + 750 7 x - 125

Solution steps

y = (\frac{x ^{\frac{1}{3}} + 5}{10})^{7}

Replace

x

with

y

x = (\frac{y ^{\frac{1}{3}} + 5}{10})^{7}

Solve for

y, x = (\frac{y ^{\frac{1}{3}} + 5}{10})^{7}

1000 x^{\frac{3}{7}} - 1500 x^{\frac{2}{7}} + 750 7 x - 125

f (x) = \frac{x - 3}{- 2 x - 4}

f (x) = 7 x^{2} + 4, x \geq 0

f (x) = - 15 x^{2} + 350 x - 200

f (x) = x - 4 - 2

f (x) = x - 4 + 8

What is the inverse of f(x)=((x^{1/3}+5)/(10))^7 ?
The inverse of f(x)=((x^{1/3}+5)/(10))^7 is 1000x^{3/7}-1500x^{2/7}+750\sqrt[7]{x}-125