Question

Find the inverse function f(x)=log₄ (2x−5)?

a) ƒ⁻¹(x)=4ˣ+5
b) ƒ⁻¹(x)= 1/2⋅4ˣ+5
c) ƒ⁻¹(x)= x+5/2
​d) ƒ⁻¹(x)= 1/2⋅(4ˣ+5)

Answer 1

The inverse function of f(x) = log4(2x - 5) is found by switching x and y, converting to exponential form, and solving for y. The correct inverse function is f¹(x) = 1/2 ⋅ (4ˣ + 5), which is option (d).

Step-by-step explanation:

The student's question involves finding the inverse function of f(x) = log4(2x - 5). To find the inverse function, one can switch the roles of x and y in the original function and solve for y. Here's the step-by-step process:

1. Let y = log4(2x - 5).
2. Switch x and y to get x = log4(2y - 5).
3. Now solve for y. To do this, express the equation in exponential form, which gives 4x = 2y - 5.
4. Add 5 to both sides to isolate the term with y: 4x + 5 = 2y.
5. Divide both sides by 2 to solve for y: y = 1/2 ⋅ (4x + 5).

Therefore, the inverse function is ƒ-1(x) = 1/2 ⋅ (4x + 5), which corresponds to option (d).