Given the function: f(x) = x2 – 2x How can you restrict the domain so that f(x) has an inverse? What is the equation of the inve
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Answer:
(b) x ≥ 1; f⁻¹(x) = 1+√(x+1)
Step-by-step explanation:
We can find the inverse function by solving for y:
x = f(y)
x = y² -2y
x +1 = y² -2y +1
x +1 = (y -1)²
√(x +1) = y -1
1 +√(x +1) = y
So, the inverse function is ...
For this, the root will be non-negative, so the minimum value of this function is 1. That is, the minimum value of x for which the original function has this as an inverse is 1.
The domain restriction is x ≥ 1.
The inverse function is f⁻¹(x) = 1+√(x+1)
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The inverse of a function f(x) is f⁻¹(x) = 4x + 3 after using the concept of the inverse of a function.
<h3>What is a function?</h3>It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
To find the inverse of a function:
Interchange the f(x) and x
f(x) → x
x → f⁻¹(x)
Make the subject f(x);
Thus, the inverse of a function f(x) is f⁻¹(x) = 4x + 3 after using the concept of the inverse of a function.
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Hi there!
f(x) = 2(1/5)ˣ
Recall the form of an exponential function:
f(x) = a(b)ˣ where:
a = initial value
b = rate of decay/growth
If b > 1, the function is undergoing exponential growth. If b < 1, then the function is undergoing exponential decay.
1/5 < 1, so the function is undergoing exponential decay, not growth.