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Find the inverse function of the function
f(x)=-(8x)/(3).

f^(-1)(x)=(3)/(8x)

f^(-1)(x)=(3x)/(8)

f^(-1)(x)=-(3x)/(8)

f^(-1)(x)=-(3)/(8x)

Find the inverse function of the function $f(x)=-\frac{8 x}{3}$ . $\newline$ $f^{-1}(x)=\frac{3}{8 x}$ $\newline$ $f^{-1}(x)=\frac{3 x}{8}$ $\newline$ $f^{-1}(x)=-\frac{3 x}{8}$ $\newline$ $f^{-1}(x)=-\frac{3}{8 x}$

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Multiplication with rational exponents

Full solution

Q. Find the inverse function of the function

f(x)=-\frac{8 x}{3}

.

\newline

f^{-1}(x)=\frac{3}{8 x}

\newline

f^{-1}(x)=\frac{3 x}{8}

\newline

f^{-1}(x)=-\frac{3 x}{8}

\newline

f^{-1}(x)=-\frac{3}{8 x}

Replace with $y$ : To find the inverse function, we start by replacing $f(x)$ with $y$ : $y = -\frac{8x}{3}$
Swap x and y: Next, we swap x and y to find the inverse function: $\newline$ $x = -\frac{8y}{3}$
Solve for y: Now, we solve for y to get the inverse function. Multiply both sides by $-\frac{3}{8}$ to isolate y: $\newline$ $y = \left(-\frac{3}{8}\right)x$
Write inverse function: We can now write the inverse function as: $f^{-1}(x) = \frac{-3}{8}x$

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