Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=2x-1 s(x)=6x write the expression for (r*s)(x) and (r-s)(x) and evaluate (r=s)(4)
r*s = (2x-1)(6x) = 12 x^2 - 6x
r(s(x)) = 2 (6x) - 1 = 12 x - 1
r(x) - s(x) = (2x-1) - 6x = -4x -1
r(x) = s(x) when 2x-1 = 6x or x = -1/4
r(4) = s(4) never
(r*s)(4) = 12 x^2 - 6 x = 12*16 - 24 = 168
pick whatever you mean
To find the expression for (r*s)(x), we need to multiply the functions r(x) and s(x).
r(x) = 2x - 1
s(x) = 6x
(r*s)(x) = r(x) * s(x)
= (2x - 1) * (6x)
Expanding the expression:
(r*s)(x) = 12x^2 - 6x
To find the expression for (r-s)(x), we need to subtract the functions r(x) and s(x).
(r-s)(x) = r(x) - s(x)
= (2x - 1) - (6x)
Expanding the expression:
(r-s)(x) = 2x - 1 - 6x
= -4x - 1
To evaluate (r=s)(4), we need to substitute 4 for x in the expression for r(x) and s(x) and check if they are equal.
r(x) = 2x - 1
s(x) = 6x
Substituting x = 4:
r(4) = 2(4) - 1
= 8 - 1
= 7
s(4) = 6(4)
= 24
(r=s)(4) means checking if r(4) is equal to s(4).
Therefore, we need to compare 7 with 24.
Since 7 is not equal to 24, the expression (r=s)(4) is false.
To find the expression for (r*s)(x), we need to multiply the two functions r(x) and s(x). The expression is given by:
(r*s)(x) = r(x) * s(x)
Substituting the given functions r(x) = 2x - 1 and s(x) = 6x:
(r*s)(x) = (2x - 1) * (6x)
Expanding this expression, we have:
(r*s)(x) = 12x^2 - 6x
To find the expression for (r-s)(x), we need to subtract s(x) from r(x). The expression is given by:
(r-s)(x) = r(x) - s(x)
Substituting the given functions r(x) = 2x - 1 and s(x) = 6x:
(r-s)(x) = (2x - 1) - (6x)
Expanding this expression, we have:
(r-s)(x) = 2x - 1 - 6x
Simplifying, we get:
(r-s)(x) = -4x - 1
To evaluate (r=s)(4), we need to substitute x = 4 into the expression for (r=s)(x):
(r=s)(4) = -4(4) - 1
Calculating this expression, we have:
(r=s)(4) = -16 - 1
Simplifying further, we get:
(r=s)(4) = -17