For the function f(x)=((x-4))/(3), find f^(-1)(x). f^(-1)(x)=((x+4))/(3) f^(-1)(x)=3(x-4) f^(-1)(x)=3(x+4) f^(-1)(x)=3x+4

Rewrite with y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. Let's start by rewriting the function with y instead of f(x): y = (x - 4) / 3Switch x and y: Now, we switch x and y to find the inverse: x = (y - 4) / 3Eliminate denominator: Next, we solve for y by multiplying both sides of the equation by 3 to eliminate the denominator: 3x = y - 4Isolate y: Then, we add 4 to both sides of the equation to isolate y: 3x + 4 = yWrite inverse function: Now that we have y by itself, we can write the inverse function: f^(-1)(x) = 3x + 4

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For the function
f(x)=((x-4))/(3), find
f^(-1)(x).

f^(-1)(x)=((x+4))/(3)

f^(-1)(x)=3(x-4)

f^(-1)(x)=3(x+4)

f^(-1)(x)=3x+4

For the function $f(x)=\frac{(x-4)}{3}$ , find $f^{-1}(x)$ . $\newline$ $f^{-1}(x)=\frac{(x+4)}{3}$ $\newline$ $f^{-1}(x)=3(x-4)$ $\newline$ $f^{-1}(x)=3(x+4)$ $\newline$ $f^{-1}(x)=3 x+4$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. For the function

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

, find

f^{-1}(x)

\newline

f^{-1}(x)=\frac{(x+4)}{3}

\newline

f^{-1}(x)=3(x-4)

\newline

f^{-1}(x)=3(x+4)

\newline

f^{-1}(x)=3 x+4

Rewrite with y: To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . Let's start by rewriting the function with $y$ instead of $f(x)$ : $\newline$ $y = \frac{x - 4}{3}$
Switch x and y: Now, we switch x and y to find the inverse: $x = \frac{y - 4}{3}$
Eliminate denominator: Next, we solve for $y$ by multiplying both sides of the equation by $3$ to eliminate the denominator: $3x = y - 4$
Isolate y: Then, we add $4$ to both sides of the equation to isolate $y$ : $3x + 4 = y$
Write inverse function: Now that we have $y$ by itself, we can write the inverse function: $f^{-1}(x) = 3x + 4$