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If $f(x)=3x-9$ , what is $f^{-1}(12)$ ?

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Evaluate expression when two complex numbers are given

Full solution

Q. If

f(x)=3x-9

, what is

f^{-1}(12)

?

Given Function: We are given the function $f(x) = 3x - 9$ and we need to find the inverse function $f^{-1}(x)$ such that $f^{-1}(12)$ gives us the $x$ -value for which $f(x) = 12$ . To find the inverse function, we need to solve for $x$ in terms of $y$ , where $y = f(x)$ . Let $y = 3x - 9$ .
Solving for x: Now we will solve the equation $y = 3x - 9$ for $x$ . Add $9$ to both sides of the equation to isolate the term with $x$ on one side. $y + 9 = 3x$
Finding Inverse Function: Next, divide both sides of the equation by $3$ to solve for $x$ . $\newline$ $\frac{y + 9}{3} = x$ $\newline$ This gives us the inverse function $f^{-1}(y) = \frac{y + 9}{3}$ .
Substitute $y$ with $12$ : Now we can find $f^{-1}(12)$ by substituting $y$ with $12$ in the inverse function. $\newline$ $f^{-1}(12) = \frac{(12 + 9)}{3}$
Perform Addition: Perform the addition inside the parentheses. $f^{-1}(12) = \frac{(21)}{3}$
Final Result: Finally, divide $21$ by $3$ to get the value of $f^{-1}(12)$ . $f^{-1}(12) = 7$

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