The ratio of the volume of fruit juice to the volume of smoothies served at a party was 4.5 to 2.4. There were 35 liters more fr
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The choices were typed wrong, but we can find the inverse of each option.
For function the inverse is the same function
, because an inverse of a function is where their composition gives the independent variable as unique result.
If we do that with each function, we have:
; where
and
, we have
So they are inverse.
For its inverse would be
, because
For , its inverse is
, because
For , its inverse is
, because
There you have all inverses. Basically, if their composition results in , that means they are inverse.
The function increases in the interval (-∞, -3) and the function also increases in the interval (-1,∞) .
The given function is of the form
f(x) = x³ + 6x² + 8x
Now we take the first differentiation of the function
f'(x) = 2x² + 12x + 8
f'(x) = 2 (x² + 6x + 9) -10
f'(x) = 2(x+3)² - 10
Therefore at x = -3 , f'(x) = -10.
Hence the function is increasing in the interval of (-∞, -3)
Again f'(x) = 2x² + 12x + 8 , so after first differentiation we get :
That the function is also increasing in the interval (-1,∞)
Now for the interval (-4,-2), we can say that the graph of the function is positive as the y value increases and then decreases but all y values are positive as illustrated in the graph.
In the interval (0,∞) the function is strictly increasing and has positive values only.
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