Is the inverse a function? g(x)=-4x+6 D yes no Write the inverse function in the form ax+b . Simplify any fractions. g^-1(x)=square

To determine if the inverse of the function $g(x) = -4x + 6$ is also a function, we need to check if the inverse function passes the vertical line test. <br /><br />Step 1: Find the inverse function.<br />To find the inverse function, we need to swap the x and y variables and solve for y.<br />$y = -4x + 6$<br />$x = -4y + 6$<br />$y = \frac{6 - x}{4}$<br /><br />So, the inverse function is $g^{-1}(x) = \frac{6 - x}{4}$.<br /><br />Step 2: Check if the inverse function is a function.<br />To check if the inverse function is a function, we need to see if it passes the vertical line test. This means that for any vertical line drawn on the graph of the inverse function, it should intersect the graph at most once.<br /><br />The graph of the inverse function $g^{-1}(x) = \frac{6 - x}{4}$ is a straight line with a negative slope. Therefore, it passes the vertical line test and is a function.<br /><br />Answer: Yes, the inverse of the function $g(x) = -4x + 6$ is also a function. The inverse function is $g^{-1}(x) = \frac{6 - x}{4}$.