The inverse of the function f(x) = 2x + 1 will be h(x) = (1/2)x – 1/2. Then the correct option is A.
What is inverse of a function?
Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
f(x) = 2x + 1
Then the inverse of the function f(x) will be
Replace the f(x) with x and replace the x with h(x). Then the equation of the function will be
x = 2h(x) + 1
Subtract 1 on both sides, then the equation of the function h(x) will be
2 h(x) + 1 – 1 = x – 1
2 h(x) = x – 1
Divide the equation by 2, then the equation of the function h(x) will be
2 h(x) = x – 1
h(x) = (x – 1) / 2
Simplify the equation, then the equation will be
h(x) = (1/2)x – 1/2
Thus, the inverse of the function f(x) = 2x + 1 will be h(x) = (1/2)x – 1/2.
Then the correct option is A.
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