For the function f(x)=x^((1)/(7))+8, find f^(-1)(x). f^(-1)(x)=(x-8)^((1)/(7)) f^(-1)(x)=x^((1)/(7))-8 f^(-1)(x)=(x-8)^(7) f^(-1)(x)=x^(7)-8

Write function as y: To find the inverse function, we first write the function as y = x^(1/7) + 8.Swap x and y: Next, we swap x and y to find the inverse function: x = y^(1/7) + 8.Solve for y: Now, we solve for y by subtracting 8 from both sides: x - 8 = y^(1/7).Isolate y: To isolate y, we raise both sides of the equation to the power of 7: (x - 8)^7 = y.Find inverse function: We have found the inverse function: f^(-1)(x) = (x - 8)^7.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the function
f(x)=x^((1)/(7))+8, find
f^(-1)(x).

f^(-1)(x)=(x-8)^((1)/(7))

f^(-1)(x)=x^((1)/(7))-8

f^(-1)(x)=(x-8)^(7)

f^(-1)(x)=x^(7)-8

For the function $f(x)=x^{\frac{1}{7}}+8$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=(x-8)^{\frac{1}{7}}$ $\newline$ $f^{-1}(x)=x^{\frac{1}{7}}-8$ $\newline$ $f^{-1}(x)=(x-8)^{7}$ $\newline$ $f^{-1}(x)=x^{7}-8$

View step-by-step help

Home

Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. For the function

f(x)=x^{\frac{1}{7}}+8

, find

f^{-1}(x)

\newline

f^{-1}(x)=(x-8)^{\frac{1}{7}}

\newline

f^{-1}(x)=x^{\frac{1}{7}}-8

\newline

f^{-1}(x)=(x-8)^{7}

\newline

f^{-1}(x)=x^{7}-8

Write function as $y$ : To find the inverse function, we first write the function as $y = x^{\frac{1}{7}} + 8$ .
Swap $x$ and $y$ : Next, we swap $x$ and $y$ to find the inverse function: $x = y^{(1/7)} + 8$ .
Solve for y: Now, we solve for y by subtracting $8$ from both sides: $x - 8 = y^{1/7}$ .
Isolate $y$ : To isolate $y$ , we raise both sides of the equation to the power of $7$ : $(x - 8)^7 = y$ .
Find inverse function: We have found the inverse function: $f^{-1}(x) = (x - 8)^7$ .