For the function f(x)=2(x-3)^((1)/(7)), find f^(-1)(x). f^(-1)(x)=(x^(7)+3)/(2) f^(-1)(x)=((x)/(2))^(7)+3 f^(-1)(x)=(x^(7))/(2)+3 f^(-1)(x)=((x+3)/(2))^(7)

Write function as y: To find the inverse function, we first write the function as y = 2(x - 3)^(1/7).Swap x and y: Next, we swap x and y to begin solving for the inverse function: x = 2(y - 3)^(1/7).Isolate y term: Now, we solve for y by isolating the term with y in it. We start by dividing both sides by 2: (x/2) = (y - 3)^(1/7).Remove exponent: To remove the exponent, we raise both sides to the power of 7: ((x/2)^7) = y - 3.Add 3: Finally, we add 3 to both sides to solve for y: y = ((x/2)^7) + 3.Find inverse function: We have found the inverse function, which is f^(-1)(x) = ((x/2)^7) + 3.

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Q. For the function

f(x)=2(x-3)^{\frac{1}{7}}

, find

f^{-1}(x)

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f^{-1}(x)=\frac{x^{7}+3}{2}

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f^{-1}(x)=\left(\frac{x}{2}\right)^{7}+3

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f^{-1}(x)=\frac{x^{7}}{2}+3

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f^{-1}(x)=\left(\frac{x+3}{2}\right)^{7}

Write function as $y$ : To find the inverse function, we first write the function as $y = 2(x - 3)^{\frac{1}{7}}$ .
Swap x and y: Next, we swap x and y to begin solving for the inverse function: $x = 2(y - 3)^{\frac{1}{7}}$ .
Isolate y term: Now, we solve for y by isolating the term with y in it. We start by dividing both sides by $2$ : $(x/2) = (y - 3)^{(1/7)}$ .
Remove exponent: To remove the exponent, we raise both sides to the power of $7$ : $((x/2)^7) = y - 3$ .
Add $3$ : Finally, we add $3$ to both sides to solve for $y$ : $y = \left(\frac{x}{2}\right)^7 + 3$ .
Find inverse function: We have found the inverse function, which is $f^{-1}(x) = \left(\frac{x}{2}\right)^7 + 3$ .