Find the inverse of the function f(x)=3x-7 Drag numbers to the blanks to complete the expression for the inverse. f^-1(x) f^-1(x)=ldots x+ -(7)/(3) (1)/(3) -(4)/(3) (3)/(7) -(3)/(7) -(1)/(3) (7)/(3)

To find the inverse of the function \( f(x) = 3x - 7 \), follow these steps:<br /><br />### Step 1: Replace \( f(x) \) with \( y \)<br />Let \( y = 3x - 7 \).<br /><br />### Step 2: Swap \( x \) and \( y \)<br />To find the inverse, interchange \( x \) and \( y \):<br />\[<br />x = 3y - 7<br />\]<br /><br />### Step 3: Solve for \( y \)<br />Rearrange the equation to isolate \( y \):<br />\[<br />x + 7 = 3y<br />\]<br />\[<br />y = \frac{x + 7}{3}<br />\]<br /><br />Thus, the inverse function is:<br />\[<br />f^{-1}(x) = \frac{x + 7}{3}.<br />\]<br /><br />### Step 4: Match the given options<br />Rewrite \( f^{-1}(x) \) as:<br />\[<br />f^{-1}(x) = \frac{1}{3}x + \frac{7}{3}.<br />\]<br /><br />From the provided options, the correct numbers to drag into the blanks are:<br />\[<br />f^{-1}(x) = \frac{1}{3}x + \frac{7}{3}.<br />\]