Question

The function f is such that f(x)=4x 7 write an expression for f^-1

Answer 1

The inverse function of f(x) = 4x + 7 is found by reversing the operations of f(x). By swapping x and y, then solving for y, we find the inverse function f-1(x) = (x - 7) / 4.

Step-by-step explanation:

The student has asked to find an expression for the inverse function of f(x) = 4x + 7. To find the inverse function, denoted f-1(x), you must essentially reverse the operations done in f(x). Here are the steps:

1. Replace f(x) with y: y = 4x + 7.
2. Swap x and y to get: x = 4y + 7.
3. Solve for y by first subtracting 7 from both sides: x - 7 = 4y.
4. Divide both sides by 4 to isolate y: (x - 7) / 4 = y.
5. Replace y with f-1(x): f-1(x) = (x - 7) / 4.

Therefore, the expression for the inverse function is f-1(x) = (x - 7) / 4.