Help please and don’t answer randomly I really need this done!!! ASAP!!! I’ll mark you brainlest!!
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Answer:
See attached for graphs
g(x) -- domain: -∞ < x < ∞; range: 0 < y < ∞
g^-1(x) -- domain: 0 < x < ∞; range: -∞ < y < ∞
Step-by-step explanation:
g(x) is an exponential decay function. Its base is 1/3, so each increase of 1 unit in x will multiply the y-value by a factor of 1/3. The graph will rapidly approach its horizontal asymptote of y=0 as x gets large. The y-intercept is (0, 1). Just as y gets smaller as x increases, so it gets larger as x decreases. Each decrease of x by 1 unit causes the y-value to be multiplied by 3.
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The graph of g^-1(x) is the graph of g(x) reflected across the line y=x. That is, each coordinate pair (x, y) on the graph of g(x) becomes a point (y, x) on the graph of the inverse function. In order to graph g^-1(x), you don't need to write down the function, you only need to know the relationship between the graphs.
Just as x- and y- are interchanged on the graph, so the domain, range, and intercepts are interchanged. g^-1(x) will have a vertical asymptote of x=0, and an x-intercept of (1, 0). The domain of g^-1(x) is the range of g(x): 0 < x < ∞; and the range of g^-1(x) is the domain of g(x): -∞ < y < ∞.
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The attached graph shows g(x) in red and g^-1(x) in blue. As you can see, we created the graph simply by interchanging x and y. The line y=x is shown for reference, so you can see that each curve is a reflection of the other across that line.
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<em>Additional comment</em>
The explicit expression for g^-1(x) can be found by solving for y:
x = g(y)
If you're familiar with the log function, you know it has an x-intercept of 1 and a vertical asymptote at x=0. The base of the log function is simply a vertical scale factor. The minus sign reflects it across the x-axis.
Answer:
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Step-by-step explanation:
Please consider the complete question.
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms. Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).
Since wrestler gained weight at a rate of 5.5 kilograms per month, so slope of line be 5.5.
Now, we will use point-slope form of equation as:
, where,
m = Slope
= Given point on the line.
Upon substituting coordinates of point (11,140) in above formula, we will get:
Therefore, our required function would be .