This week, Michael collected $468 for delivering newspapers. He had 40 repeat customers and 18 new ones. As an incentive, he cha
1 answer:
You might be interested in
<u>ANSWER</u>
<u>EXPLANATION</u>
Given
and
We want to find
This means we substitute the function in to another function
and evaluate.
This implies that;
We expand the parenthesis to obtain;
We simplify further to obtain;
Hence the correct answer is A
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.
__
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 < ∞.
__
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.
_____
<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.
Hey there
Lets solve this question together,
Convert <span>76.8%</span><span> to a decimal.
</span>
Multiply 0.768<span> by </span>x<span> to get </span><span>0.768x</span><span>.
</span>
Multiply<span> each </span>term<span> by </span><span>1 / 0.768</span><span> and simplify.
</span>
Cancel the common factor of 0.768.
Divide 40.32<span> by </span>0.768<span> to get </span><span>52.5
</span>
<span>
</span>
Lets solve this question together,
Convert <span>76.8%</span><span> to a decimal.
</span>
Multiply 0.768<span> by </span>x<span> to get </span><span>0.768x</span><span>.
</span>
Multiply<span> each </span>term<span> by </span><span>1 / 0.768</span><span> and simplify.
</span>
Cancel the common factor of 0.768.
Divide 40.32<span> by </span>0.768<span> to get </span><span>52.5
</span>
</span>