Final answer:
To find the inverse of f(x) = 6x - 7, we solve for x in terms of y and switch x and y, yielding the inverse function f^-1(x) = (x + 7) / 6, which is answer choice a). This is verified by checking that the inverse function, when substituted into the original, gives the identity function.
Step-by-step explanation:
The given function f(x) = 6x - 7 can be inverted by following a series of algebraic steps. To find the inverse function, which we'll call f-1(x), we need to solve for x in terms of y, and then interchange the roles of x and y.
- Start with the original equation, replacing f(x) with y: y = 6x - 7.
- Rearrange the equation to solve for x: x = (y + 7) / 6.
- Now, switch x and y to get the inverse function: f-1(x) = (x + 7) / 6. This means that the correct answer is a) (x + 7) / 6.
To ensure that this is the correct inverse, we can eliminate terms and simplify the algebra by plugging the inverse function back into the original and confirming that it gives us the identity function, which would be x. This is a method to check the answer to see if it is reasonable and verifies that the inverse function is indeed the right one.