If the function f(x)=mx+b has an inverse function, which statement must be true
2 answers:
The things we know that are true based on this is that m does not equal 0 and the inverse function is f(x) = .
We know that the slope is not 0, because there is no inverse function if this is the case.
Secondly, we can find the inverse function by switching f(x) and x and solving for the new f(x). The work for this is below.
f(x) = mx + b ----> switch f(x) and x
x = mf(x) + b ----> subtract b
x - b = mf(x) ----> divide by m
f(x) = .
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We are given : Distance of the swing = 100 feet.
Distance of slide = 80 feet.
Angle between swing and slide = 30 degrees.
We need to find the distance between the swing and the slide.
Distance of swing, distance of slide and distance between the swing and the slide form a triangle.
We can apply cosine law to find the distance between the swing and the slide.
c^2 = a^2 +b^2 - 2ab cos C
c^2 = 100^2 +80^2 - 2(100)(80) cos 30°
c^2 = 10000 + 6400 -2* 8000
c^2 = 16400 - 8000
c^2 = 16400 - 13856
c^2 = 2544
c= 50.44
c = 50 feet approximately.
<h3>Therefore, the approximate distance between the swing and the slide is 50 feet.</h3>