You have a definition for f(x) f(x) = (7x+9)/(x-5) So to find f(y), you put "y" everywhere you see "x" in f(x) f(y) = (7y+9)/(y-5) You are asked to equate this to x and solve for y f(y) = x (7y+9)/(y-5) = x 7y + 9 + x(y - 5) (multiply by y-5) 7y + 9 = xy - 5x (eliminate the parentheses using the distributive property) From here, we will put all term containing y on one side of the equal sign, and all terms not containing y on the other side. 7y + 9 + 5x = xy (add 5x) 9 + 5x = xy - 7y (subtract 7y) 9 + 5x = y(x - 7) (factor right side) (9+5x)/(x-7) = y (divide by the y coefficient)
The desired solution is y = (5x+9)/(x-7).
This process finds the inverse function of the function f(x). The inverse of f(x) is denoted by f -1(x). It tells the value of x required to make f(x) be something in particular. Example Suppose we want to find the value of x that will make f(x) = -4. We can use our inverse function f -1(x) = (5x+9)/(x-7) to find it. F -1(-4) = (5(-4)+9)/((-4)-7) = (-20+9)/(-11) = -11/-11 = 1 We can verify this to be what we were looking for by evaluating f(1) f(1) = (7(1)+9)/((1)-5) = (7+9)/(-4) = 16/-4 = -4 We wanted to find the value of x that would make f(x) = -4. Using our inverse function, we found x=1 would do it, and we verified that f(1) = -4.
The desired solution is y = (5x+9)/(x-7).
This process finds the inverse function of the function f(x). The inverse of f(x) is denoted by f -1(x). It tells the value of x required to make f(x) be something in particular. Example Suppose we want to find the value of x that will make f(x) = -4. We can use our inverse function f -1(x) = (5x+9)/(x-7) to find it. F -1(-4) = (5(-4)+9)/((-4)-7) = (-20+9)/(-11) = -11/-11 = 1 We can verify this to be what we were looking for by evaluating f(1) f(1) = (7(1)+9)/((1)-5) = (7+9)/(-4) = 16/-4 = -4 We wanted to find the value of x that would make f(x) = -4. Using our inverse function, we found x=1 would do it, and we verified that f(1) = -4.
