Given the function f (x) = 9x + 7, find its inverse.
let y = 9x+7
the inverse is x = 9y+7
solving this for y
9y= x-7
y = (x-7)/9 <------ that's the inverse
or
f^-1 (x) = (x-7)/9
To find the inverse of a function, we need to switch the x and y variables and solve for y.
Step 1: Start with the given function: f(x) = 9x + 7
Step 2: Replace f(x) with y: y = 9x + 7
Step 3: Swap x and y: x = 9y + 7
Step 4: Solve for y: Subtract 7 from both sides of the equation: x - 7 = 9y
Step 5: Divide both sides of the equation by 9 to isolate y: (x - 7)/9 = y
Step 6: Replace y with f^(-1)(x), the inverse function: f^(-1)(x) = (x - 7)/9
Therefore, the inverse function of f(x) = 9x + 7 is f^(-1)(x) = (x - 7)/9.
To find the inverse of a function, we need to swap the x and y variables and then solve for y.
Step 1: Replace f(x) with y:
f(x) = 9x + 7 ---> y = 9x + 7
Step 2: Swap x and y variables:
x = 9y + 7
Step 3: Solve for y:
x - 7 = 9y
Step 4: Divide both sides by 9:
(x - 7)/9 = y
Therefore, the inverse function of f(x) = 9x + 7 is f^(-1)(x) = (x - 7)/9.