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2 answers:
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Answer:
(-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)
Step-by-step explanation:
To make it easier to differentiate, we'll rewrite the function as ...
h(x) = 2/(x-5) -1/(x-2)
Then the derivative is ...
h'(x) = -2/(x-5)^2 +1/(x-2)^2
This will be zero when ...
-2(x-2)^2 +(x-5)^2 = 0
-2(x^2 -4x +4) +(x^2 -10x +25) = 0
-x^2 -2x +17 = 0
x^2 +2x +1 = 17 +1
x +1 = ±√18 = ±3√2
x = -1 ±3√2
The values of the function at these locations are ...
h(-1-3√2) = -1 +(2/3)√2 ≈ -1.9428
h(-1+3√2) = -1 -(2/3)√2 ≈ -0.0572
Then the range of h(x) is ...
(-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)
Answer:
1. Option D is correct.
2. Option B is correct.
3. Option B is correct.
Step-by-step explanation:
Inverse function defined as the the function that undergoes the action of the other function.
A function is the inverse of f if whenever y =f(x) and
To find the inverse of the function:
Q1.
Given the function: f(x) = 7x -1
Put y for f(x) and solve for x;
y= 7x -1
Add 1 both sides we get;
y + 1 = 7x
Divide both sides by 7 we get;
Put for x;
Interchange y =x, we have
Q 2.
Given the function:
Put y for f(x) and solve for x;
Add 7 both sides we get;
taking cube root both sides we get
Put for x;
Interchange y =x, we have
Q3 .
Given the function:
Put y for f(x) and solve for x;
Add 3 both sides we get;
Divide both sides by 5 we get;
taking cube root both sides we get
Put for x;
Interchange y =x, we have