Final answer:
The inverse of the function f(x)=3x+7 is found by first substituting y for f(x), swapping x and y, and then solving for y to get y = (x-7)/3. Thus, the inverse function is f⁻¹(x) = 1/3(x-7), which is option a).
Step-by-step explanation:
The inverse of a function can be found by swapping the x and y variables and solving for y. If f(x)=3x+7, to find the inverse of f(x), we need to reverse its operation. We start by replacing f(x) with y:
y = 3x + 7
To find the inverse, we swap x and y and then solve for y:
x = 3y + 7
Subtract 7 from both sides:
x - 7 = 3y
Finally, divide both sides by 3 to solve for y:
(x - 7)/3 = y
Thus, the inverse function, written as f⁻¹(x), is:
f⁻¹(x) = 1/3(x - 7)
Therefore, the answer that represents the inverse of f(x)=3x+7 is option a) 1/3(x−7).