Answer:
D x-1 x≠4
Step-by-step explanation:
x^2 +3x-4
-----------------
x+4
We know that x cannot equal 4 since the denominator would go to zero
Factor the numerator
(x+4) (x-1)
-----------------
x+4
Cancel like terms (x+4)
x-1 x≠4
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The inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)
<h3>How to determine the inverse relation?</h3>
The function is given as
f(x)=1/3x^2-3x+5
Start by rewriting the function in vertex form
f(x) = 1/3(x - 9/2)^2 -7/4
Rewrite the function as
y = 1/3(x - 9/2)^2 -7/4
Swap x and y
x = 1/3(y - 9/2)^2 -7/4
Add 7/4 to both sides
x + 7/4= 1/3(y - 9/2)^2
Multiply by 3
3x + 21/4= (y - 9/2)^2
Take the square roots
y - 9/2 = √(3x + 21/4)
This gives
y = 9/2 + √(3x + 21/4)
Hence, the inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)
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Answer:
Option b is right.
Step-by-step explanation:
A function is given as
Limit is to be found out for x tends to infinity.
We find that numerator and denominator has the same degree.
HEnce a horizontal asymptote exists
COefficients of leading terms are 1 and 1 respectively
Asymtote would be y =1/11 = 1
Alternate method:
When x tends to infinity, 1/x tends to 0
by dividing both numerator and denominator by square of x.
Now take limit as 1/x tends to 0
we get
limit is y tends to 1/1 =1
Hence horizontal asymptote is y =1
