What is the inverse of the function \( g(x)=5(x-2) \) \( g^{-1}(x)=\square \)

To find the inverse of the function \( g(x) = 5(x - 2) \), we start by replacing \( g(x) \) with \( y \): \[ y = 5(x - 2) \] Next, we solve for \( x \): \[ y = 5x - 10 \] Rearranging gives: \[ 5x = y + 10 \] Dividing both sides by 5 gives: \[ x = \frac{y + 10}{5} \] Now, we replace \( y \) with \( x \) to find the inverse: \[ g^{-1}(x) = \frac{x + 10}{5} \] So, the inverse function is: \[ g^{-1}(x) = \frac{x + 10}{5} \] Now, as a side note, did you know that finding an inverse function gives you a new perspective? It's like flipping a pancake! You can see the original function in a whole new way. When you apply \( g^{-1} \) to \( g(x) \), you essentially return to your starting point—just like when you flip a pancake back to its uncooked side! Additionally, a common mistake when finding inverses is forgetting to switch the roles of \( x \) and \( y \) at the right point, which can lead to quite the culinary catastrophe in your equations! Just remember to carefully invert those variables and you'll be serving up deliciously accurate outputs in no time!