Is the inverse a function? f(x)=sqrt [3](x-3) D yes no Write the inverse function in the form a(bx+c)^3+d , where a, b , c, and d are constants . Simplify any fractions. f^-1(x)=square

To determine if the inverse of the function $f(x) = \sqrt[3]{x-3}$ is also a function, we need to check if the inverse function passes the vertical line test. <br /><br />The vertical line test states that if any vertical line intersects the graph of a function at more than one point, then the function is not a function. <br /><br />In this case, the function $f(x) = \sqrt[3]{x-3}$ is a cube root function shifted 3 units to the right. The graph of this function is a curve that passes the vertical line test, meaning it is a function.<br /><br />To find the inverse function, we need to swap the x and y variables and solve for y. <br /><br />Let's start by replacing $f(x)$ with $y$:<br />$y = \sqrt[3]{x-3}$<br /><br />Now, we'll swap the x and y variables:<br />$x = \sqrt[3]{y-3}$<br /><br />To solve for y, we'll cube both sides of the equation:<br />$x^3 = y-3$<br /><br />Finally, we'll add 3 to both sides to isolate y:<br />$y = x^3 + 3$<br /><br />So, the inverse function is $f^{-1}(x) = x^3 + 3$.<br /><br />Therefore, the answer is:<br />D yes<br />$f^{-1}(x) = x^3 + 3$