Question
What is the inverse of f if f(x)=3 sqrt x-5
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GPT 3.5
To find the inverse of f(x) = 3√(x - 5), we need to switch the roles of x and f(x) and solve for x.
Let y = f(x):
y = 3√(x - 5)
To find the inverse, we solve for x:
x = 3√(y - 5)
Now, we need to isolate y:
x/3 = √(y - 5)
Squaring both sides to eliminate the square root:
(x/3)^2 = (y - 5)
Simplifying:
x^2/9 = y - 5
Adding 5 to both sides:
x^2/9 + 5 = y
Thus, the inverse of f(x) = 3√(x - 5) is:
f^(-1)(x) = x^2/9 + 5
Let y = f(x):
y = 3√(x - 5)
To find the inverse, we solve for x:
x = 3√(y - 5)
Now, we need to isolate y:
x/3 = √(y - 5)
Squaring both sides to eliminate the square root:
(x/3)^2 = (y - 5)
Simplifying:
x^2/9 = y - 5
Adding 5 to both sides:
x^2/9 + 5 = y
Thus, the inverse of f(x) = 3√(x - 5) is:
f^(-1)(x) = x^2/9 + 5
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