00:01
Hello! so, um, for the first one, g inverse of 7, well, the inverse function is just going to swap the domain and range, so, um, the domain are going to swap, so that means that 7 becomes, when 7 is the input, the output then is 8, right? because we have that a point, um, on g of x is going to be the point 8 comma 7, that means on the inverse we have the point 7 comma 8, so when the input is 7, g inverse of 7, what's the output? well, the output is 8, so g inverse of 7 is going to be equal to 8, and then we want to find, uh, what is h inverse of x? well, h of x is the function, uh, negative 2x minus 3.
00:46
To find the inverse, we can basically swap the, um, x and the y, or put it, set it equal to y, then swap the x and the y, so we have x is equal to negative 2y minus 3, and then solving for y, we'd add 3 to both sides, so we get that x plus 3 is going to be equal to negative 2y, dividing through the negative 2, we get x plus 3 over negative 2 is y, or we get negative, um, x plus 3 over 2 is equal to y, which is then the inverse, so this is going to be our inverse function, um, and then that's going to be, we can write this as e to the y, this is equal to h inverse of x, and then we find h, well, h inverse composed with h...