Which function has an inverse that is a function?
2 answers:
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Answer:
The line x = 8 is our vertical asymptote
The limit of as x approaches 8 from the left is negative infinity; -∞
Step-by-step explanation:
We have been given the following function;
Considering that the function is rational, it will defined everywhere on the real line except where the expression in the denominator will be 0;
That is the function will not be defined where;
x - 8 = 0
solving for x yields;
x = 8
The function will be approaching the vertical line x = 8 asymptotically, meaning that the function will never touch or cross this line. We can therefore say that,
The line x = 8 is our vertical asymptote for the given function
The limit of as x approaches 8 from the left;
For x approaching 8 from the left, which implies that
The denominator will be a negative quantity approaching 0 from the left, that is -∞.
Thus;
= -∞
Find the graph attached.
Answer: the height of the pole is 16.1 m.
Step-by-step explanation:
The scenario is illustrated in the attached photo.
x represents the height of the pole.
y represents the distance from the foot of one stabilizing wire to the foot of the pole.
30 - y represents the distance from the foot of the other stabilizing wire to the foot of the pole.
In solving the triangles, we would apply the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side.
Considering triangle ACD,
Tan 60 = x/y
x = ytan60 = y × 1.732
x = 1.732y- - - - - - - - -1
Considering triangle BCD,
Tan 38 = x/(30 - y)
x = (30 - y)tan38 = 0.781(30 - y)
x = 23.43 - 0.781y- - - - - - - - -2
Substituting equation 1 into equation 2, it becomes
1.732y = 23.43 - 0.781y
1.732y + 0.781y = 23.43
2.513y = 23.43
y = 23.43/2.513
y = 9.3
x = 1.732y = 1.732 × 9.3
x = 16.1 m
