Answer:
x = - 2, x = 9
Step-by-step explanation:
Given
f(x) =
The denominator of f(x) cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the values that x cannot be.
x² - 7x - 18 = 0
(x - 9)(x + 2) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 9 = 0 ⇒ x = 9
The excluded values are x = - 2, x = 9
The actual inverse function is:
And the domain is [0, ∞).
<h3>Where is the mistake?</h3>
Remember that for a given function f(x) with a domain D and a range R.
For the inverse function, f⁻¹(x) the domain is R and the range is D.
Here, for the given function the domain is x ≥ 3 and the range is [0, ∞).
Then for the inverse function, which is:
(to check this, you must have that):
The domain will be [0, ∞) and the range x ≥ 3
If you want to learn more about inverse functions:
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