(fog)(x) and (gof)(x) f(x)= 8/1-5x g(x)= 1/x Then find the domain for each
1 answer:
To find FoG ( or F of G) you put the equation of G in for the X of F
FoG =
The domain is All Except 5 since it makes the bottom 0
GoF =
The domain is -Infinity to Infinity
FoG --- The picture --- You want the denominator the same for both of the numbers. By turning 1 into 1x/x it still stays 1 because the x's cancel out, but it can group with the 5.
Next you can multiply both sides (top and bottom) by x and get the final product.
GoF --- Multiply both sides by 5x+1 and get the final product
FoG =
GoF =
FoG --- The picture --- You want the denominator the same for both of the numbers. By turning 1 into 1x/x it still stays 1 because the x's cancel out, but it can group with the 5.
Next you can multiply both sides (top and bottom) by x and get the final product.
GoF --- Multiply both sides by 5x+1 and get the final product
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The intercepts and the graph on your worksheet are not correct. Please see below for details:
has solutions at x=-1 and x=3 (use the quadratic formula to solve). That means these are the x-intercepts, namely points:
(-1,0) and (3,0).
The y-intercept comes from setting x=0 and calculating the y value:
so the y-intercept is (0,-3).
Now to the graph: Based on the form of the function we can see this is a quadratic function and its graph will be a parabola. You can reformat the expression in the following form
and that will indicate that the apex of the parabola (open up) will be at the point (1,-4).
Knowing the apex, the x intercepts, and the y intercept, we can graph it now.
Graph is in the image attached.
