If f(x) = 1 / (3x – 5), what is the inverse of f?Question 2Select one:a.1 / (3x + 5)b.1 / (3x – 5)c.(1/3).(1/x – 5)d.(1/3).(1/x + 5) e.None of these
Question
If f(x) = 1 / (3x – 5), what is the inverse of f?Question 2Select one:a.1 / (3x + 5)b.1 / (3x – 5)c.(1/3).(1/x – 5)d.(1/3).(1/x + 5) e.None of these
Solution
To find the inverse of f(x) = 1 / (3x - 5), we need to switch the roles of x and f(x) and solve for x.
Step 1: Replace f(x) with y. y = 1 / (3x - 5)
Step 2: Swap x and y. x = 1 / (3y - 5)
Step 3: Solve for y. Multiply both sides by (3y - 5): x(3y - 5) = 1
Distribute: 3xy - 5x = 1
Add 5x to both sides: 3xy = 1 + 5x
Divide both sides by 3x: y = (1 + 5x) / (3x)
So, the inverse of f(x) = 1 / (3x - 5) is g(x) = (1 + 5x) / (3x).
Therefore, the correct answer is e. None of these.
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