Question

Given f(x), which function is the inverse?

f(x) = 3x - 5
A) g(y) = 3y + 5
B) g(y) = // +5
C) g(y) = 3+5 3
D) g(y) = 5y 3​

Answer 1

g(y) = 1/3y + 5/3

Explanation:

We know that f(x) is synonymous with y so we can rewrite f(x) as y = 3x -5

To find the inverse of the function, we can switch y with x and x with y:

x = 3y - 5

Now we can isolate y to find the inverse of f(x):

(x = 3y - 5) + 5

(x + 5 = 3y) / 3

x/3 + 5/3 = y

1/3x + 5/3 = y

Thus, the inverse of f(x) is f^-1(x) = 1/3x + 5/3. Since we want to write the inverse in terms of y, we get g(y) = 1/3y + 5/3.

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