Finding inverse and stating its domain.
f(x)=3x-2/x+5
I'd switch the x and y and then solve for y. x=3y-2/y+5
x(y+5)=3y-2*y+5/y+5 Once you get the function there you would cancel out the y+5. So once you figure that out you would switch the 5 around to negative 5 and put it where the 3 was. After you do that you would keep everything else, except you put the three in place of the 5. So that would give you f(x) = -5x - 2 / x-3. Once you have the inverse you'd look at the denominator and see x-3. And since you can't have 0 in the denominator you'd know that the domain is All Real numbers except x can't equal 3.
f(x) = 2x+3
For this one i would switch the symbols, so i would end up dividing by two instead of multiplying and then i would end up subtracting three. So it would be f(x) = x-3/2. So the domain would be x> -3.
Minimum and Maximum with increasing and decreasing.
For finding the Increasing and decreasing, you would find the points on the graph. Once you do that, the points that sink low like points A and C would be increasing, because the graph goes up from there, and the points that are up high like point B would be decreasing because the graph would go down from there. As for finding the maximums and minimums it would be the opposite, because the points that are higher would be the highest points on the graph like Point B. While the lowest points on the graph would be the minimums like A and C. So the increasing points and Minimum points would be the ones on A and C, while the decreasing point and maximum point would be the one on B.
f/g(x) and f o g(x)
f(x) = x^2 g(x) = Sq. root of 9-x^2
x^2/9-x^2 So for this I would plug the square root of 9-x^2 into the x for X^2 and then plug in x^2 into the x of the square root of 9-X^2. Once that is done I would divide from there. and then after I would divide it then I would simplify it to get the final answer. And that would be x or 1.
f(g(0)) For solving this, you would plug zero into each function, so (0)^2 and the Sq. root of 9-(0)^2. once you have that you would find the solution which would be three. once I know that solution is three then I would plug that number into the function again to get my final answer. And in the case of this problem it would be f(3)*f(3)^2.
f(x)=3x-2/x+5
I'd switch the x and y and then solve for y. x=3y-2/y+5
x(y+5)=3y-2*y+5/y+5 Once you get the function there you would cancel out the y+5. So once you figure that out you would switch the 5 around to negative 5 and put it where the 3 was. After you do that you would keep everything else, except you put the three in place of the 5. So that would give you f(x) = -5x - 2 / x-3. Once you have the inverse you'd look at the denominator and see x-3. And since you can't have 0 in the denominator you'd know that the domain is All Real numbers except x can't equal 3.
f(x) = 2x+3
For this one i would switch the symbols, so i would end up dividing by two instead of multiplying and then i would end up subtracting three. So it would be f(x) = x-3/2. So the domain would be x> -3.
Minimum and Maximum with increasing and decreasing.
For finding the Increasing and decreasing, you would find the points on the graph. Once you do that, the points that sink low like points A and C would be increasing, because the graph goes up from there, and the points that are up high like point B would be decreasing because the graph would go down from there. As for finding the maximums and minimums it would be the opposite, because the points that are higher would be the highest points on the graph like Point B. While the lowest points on the graph would be the minimums like A and C. So the increasing points and Minimum points would be the ones on A and C, while the decreasing point and maximum point would be the one on B.
f/g(x) and f o g(x)
f(x) = x^2 g(x) = Sq. root of 9-x^2
x^2/9-x^2 So for this I would plug the square root of 9-x^2 into the x for X^2 and then plug in x^2 into the x of the square root of 9-X^2. Once that is done I would divide from there. and then after I would divide it then I would simplify it to get the final answer. And that would be x or 1.
f(g(0)) For solving this, you would plug zero into each function, so (0)^2 and the Sq. root of 9-(0)^2. once you have that you would find the solution which would be three. once I know that solution is three then I would plug that number into the function again to get my final answer. And in the case of this problem it would be f(3)*f(3)^2.