Answer:
D
Step-by-step explanation:
We are given the function:
[tex]\displaystyle f(x) = \frac{1}{3} x + 2[/tex]
And we want to find its inverse h.
To find the inverse of a function, we can switch the y and x variables and solve for the new y. This will be our inverse.
We begin with:
[tex]\displaystyle f(x) = y = \frac{1}{3} x+ 2[/tex]
Switching the variables yield:
[tex]\displaystyle x = \frac{1}{3}y + 2[/tex]
And solving for y yields that:
[tex]\displaystyle y = h(x) = 3x - 6[/tex]
In conclusion, the inverse function to f is 3x - 6. Our answer is D.
To understand why we switch the variables, recall that by the definition of inverse functions, if f(a) = b, then f⁻¹(b) = a. So, by switching the variables, we are essentially solving for f⁻¹(x).
