+267 The graphs of a function f(x)=3x+b and its inverse function f^{-1}(x) intersect at the point (-3,a). Given that b and a are both integers, what is the value of a?
Please i need quick help thanks :D
+23252 The function f(x) = 3x + b can be written as y = 3x + b.
To find the inverse of this function:
1) interchange the x and y terms: x = 3y + b
2) solve for y: x - b = 3y ---> 3y = x - b ---> y = (x - b) / 3
To find where they intersect, set the two functions equal to each other: 3x + b = (x - b) / 3
and, since they intersect at the point (-3, a), replace x by -3: 3(-3) + b = (-3 - b) / 3
-9 + b = (-3 - b) / 3
-27 + 3b = -3 - b
4b = 24
b = 6
So, the original function is y = 3x + 6 while the inverse is y = (x - 6) / 3
Replace the x in either function with -3 and you get that y = -3, so a = -3.
+577 well the way it is described, the lines are locked to intersect along the y axis, so they can't intersect at anything with an x value that is not equal to 0, so there is no solution.
+23252 The function f(x) = 3x + b can be written as y = 3x + b.
To find the inverse of this function:
1) interchange the x and y terms: x = 3y + b
2) solve for y: x - b = 3y ---> 3y = x - b ---> y = (x - b) / 3
To find where they intersect, set the two functions equal to each other: 3x + b = (x - b) / 3
and, since they intersect at the point (-3, a), replace x by -3: 3(-3) + b = (-3 - b) / 3
-9 + b = (-3 - b) / 3
-27 + 3b = -3 - b
4b = 24
b = 6
So, the original function is y = 3x + 6 while the inverse is y = (x - 6) / 3
Replace the x in either function with -3 and you get that y = -3, so a = -3.
